﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Organization and Basis of Presentation</ReportName>
  <ReportLongName>0201 - Disclosure - Organization and Basis of Presentation</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="6 Months Ended" />
        <Label Id="2" Label="Jun. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDEPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Organization and Basis of Presentation [Abstract]</Label>
      <Level>0</Level>
      <ElementName>us-gaap_GeneralPoliciesAbstract</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Organization and Basis of Presentation</Label>
      <Level>1</Level>
      <ElementName>us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>verboselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 1 - us-gaap:OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock--&gt;
   &lt;div align="left" style="margin-left: 0%"&gt;&lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;!-- XBRL Pagebreak End --&gt;
   &lt;/div&gt;&lt;!-- END PAGE WIDTH --&gt;
   &lt;div align="left" style="margin-left: 0%"&gt;&lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;&lt;/div&gt;
   &lt;/div&gt;&lt;!-- END PAGE WIDTH --&gt;
   &lt;div align="left" style="margin-left: 0%"&gt;&lt;!-- XBRL,ns --&gt;
   &lt;!-- xbrl,nx --&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;&lt;/div&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 12pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;Note&amp;#160;1&amp;#160;&amp;#8212;&amp;#160;Organization
       and Basis of Presentation&lt;/font&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 2%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       &lt;b&gt;&lt;i&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;Organization&lt;/font&gt;&lt;/i&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       Copano Energy, L.L.C., a Delaware limited liability company, was
       formed in August 2001 to acquire entities owning businesses
       operating under the Copano name since 1992. We, through our
       subsidiaries, provide midstream services to natural gas
       producers, including natural gas gathering, compression,
       dehydration, treating, marketing, transportation, processing,
       conditioning and fractionation services. Our assets are located
       in Oklahoma, Texas, Wyoming and Louisiana. &lt;i&gt;Unless the context
       requires otherwise, references to &amp;#8220;Copano,&amp;#8221;
       &amp;#8220;we,&amp;#8221; &amp;#8220;our,&amp;#8221; &amp;#8220;us&amp;#8221; or like terms
       refer to Copano Energy, L.L.C., its subsidiaries and entities it
       manages or operates&lt;/i&gt;.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       Our natural gas pipelines collect natural gas from wellheads or
       designated points near producing wells and deliver these volumes
       to our processing plants, third-party processing plants,
       third-party pipelines, local distribution companies, power
       generation facilities and industrial consumers. Our processing
       plants take delivery of natural gas from our gathering systems
       as well as third-party pipelines. The natural gas is then
       treated as needed to remove contaminants and then conditioned or
       processed to extract mixed natural gas liquids
       (&amp;#8220;NGLs&amp;#8221;). After treating and processing or
       conditioning, we deliver the residue gas primarily to
       third-party pipelines through plant interconnects and sell the
       NGLs, in some cases after separating the NGLs into select
       component products, to third parties through our plant
       interconnects or our NGL pipelines. We refer to our operations
       (i)&amp;#160;conducted through our subsidiaries operating in
       Oklahoma, including our crude oil pipeline which was sold in
       October 2009, collectively as our &amp;#8220;Oklahoma&amp;#8221; segment,
       (ii)&amp;#160;conducted through our subsidiaries operating in Texas
       and Louisiana collectively as our &amp;#8220;Texas&amp;#8221; segment and
       (iii)&amp;#160;conducted through our subsidiaries operating in
       Wyoming collectively as our &amp;#8220;Rocky Mountains&amp;#8221; segment.
   &lt;/div&gt;
   &lt;div style="margin-top: 12pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 2%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
       &lt;b&gt;&lt;i&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;Basis
       of Presentation and Principles of Consolidation&lt;/font&gt;&lt;/i&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       The accompanying unaudited consolidated financial statements and
       related notes include our assets, liabilities and results of
       operations for each of the periods presented. All intercompany
       accounts and transactions are eliminated in our unaudited
       consolidated financial statements.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       Because we sold our crude oil pipeline operations in October
       2009, the results related to these operations have been
       classified as &amp;#8220;discontinued operations&amp;#8221; on the
       accompanying unaudited consolidated statements of operations for
       the three and six months ended June&amp;#160;30, 2009. Unless
       otherwise indicated, information about the statements of
       operations that is presented in the notes to unaudited
       consolidated financial statements relates only to our continuing
       operations. See Note&amp;#160;13 for additional details.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       The accompanying unaudited consolidated financial statements
       have been prepared without audit pursuant to the rules and
       regulations of the Securities and Exchange Commission
       (&amp;#8220;SEC&amp;#8221;). Accordingly, our financial statements reflect
       all normal and recurring adjustments that are, in the opinion of
       our management, necessary for a fair presentation of our results
       of operations for the interim periods. Certain information and
       notes normally included in financial statements prepared in
       accordance with generally accepted accounting principles have
       been condensed or omitted pursuant to such rules and regulations.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
       However, our management believes that the disclosures are
       adequate to make the information presented not misleading. In
       the preparation of these financial statements, we evaluated
       subsequent events through the issuance date of the financial
       statements. These interim financial statements should be read in
       conjunction with the audited consolidated financial statements
       and notes thereto contained in our Annual Report on
       &lt;font style="white-space: nowrap"&gt;Form&amp;#160;10-K&lt;/font&gt;
       and Amendment No.&amp;#160;1 for the year ended December&amp;#160;31,
       2009.
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak Begin --&gt;
   &lt;/div&gt;
   &lt;!-- END PAGE WIDTH --&gt;
   &lt;!-- PAGEBREAK --&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;b&gt;
   &lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;
   &lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;
   &lt;/div&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: #ffffff"&gt;
   &lt;b&gt;
   &lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;
   &lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak End --&gt;
   &lt;/div&gt;
</NonNumbericText>
          <NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>Description containing the entire organization, consolidation and basis of presentation of financial statements disclosure. May be provided in more than one note to the financial statements, as long as users are provided with an understanding of (1) the significant judgments and assumptions made by an enterprise in determining whether it must consolidate a VIE and/or disclose information about its involvement with a VIE, (2) the nature of restrictions on a consolidated VIE's assets reported by an enterprise in its statement of financial position, including the carrying amounts of such assets, (3) the nature of, and changes in, the risks associated with an enterprise's involvement with the VIE, and (4) how an enterprise's involvement with the VIE affects the enterprise's financial position, financial performance, and cash flows.  Describes procedure if disclosures are provided in more than one note to the financial statements.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name FASB Staff Position (FSP)
 -Number FAS140-4 and FIN46(R)-8
 -Paragraph 8, C1, C7

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Accounting Research Bulletin (ARB)
 -Number 51
 -Paragraph 2-6

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Statement of Position (SOP)
 -Number 94-6
 -Paragraph 10

Reference 4: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name FASB Interpretation (FIN)
 -Number 46R
 -Paragraph 4, 14, 15

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
