<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>106 - Disclosure - Organization, Operations and Basis of Accounting</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>P01_01_2013To06_30_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001124608</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Organization, Consolidation and Presentation of Financial Statements [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="P01_01_2013To06_30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>              &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif "&gt;  &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;BACKGROUND-COLOR: transparent; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  &lt;strong&gt;1. Organization, Operations and Basis of  Accounting&lt;/strong&gt;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  Response Genetics, Inc. (the &amp;#8220;Company&amp;#8221;) was  incorporated in the State of Delaware on September 23, 1999 as Bio  Type, Inc. for the purpose of providing molecular profiling  services of tumor tissue that has been formalin-fixed and embedded  in paraffin. In August 2000, the Company changed its name to  Response Genetics, Inc.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  The Company is a life science company engaged in the research,  development, marketing and sale of pharmacogenomics-clinical  diagnostic tests for cancer. Pharmacogenomics is the science of how  an individual&amp;#8217;s genetic makeup relates to drug response.  Diagnostic tests based on pharmacogenomics facilitate the  prediction of a response to drug therapy or survival following  surgery based on an individual&amp;#8217;s genetic makeup. In order to  generate pharmacogenomic information from patient specimens for  these tests, the Company uses its proprietary technologies that  enable the Company to reliably and consistently extract ribonucleic  acid (&amp;#8220;RNA&amp;#8221;) and deoxyribonucleic acid  (&amp;#8220;DNA&amp;#8221;) from tumor specimens that are stored as  formalin-fixed and paraffin-embedded (&amp;#8220;FFPE&amp;#8221;) specimens  and, thereby to analyze genetic information contained in these  tissues for each patient. The Company&amp;#8217;s platforms include  analysis of single biomarkers using the polymerase chain reaction  method as well as global gene interrogation using microarray  methods and fluorescence in situ hybridization (&amp;#8220;FISH&amp;#8221;)  from paraffin or frozen tissue specimens. The Company primarily  derives its revenue from the sale of its ResponseDX&lt;sup&gt;&amp;#174;&lt;/sup&gt;  diagnostic testing products and by providing pharmacogenomic  clinical trial testing services to pharmaceutical companies in the  United States, Asia and Europe.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  The Company&amp;#8217;s goal is to provide cancer patients and their  physicians with a means to make informed, individualized treatment  decisions based on genetic analysis of tumor tissues. The  Company&amp;#8217;s pharmacogenomic analysis of clinical trial  specimens for the pharmaceutical industry may provide data that  will lead to a better understanding of the molecular basis for  response to specific drugs and, therefore lead to individualized  treatment.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  Since its inception, the Company has devoted substantial effort in  developing its products and has incurred losses and negative cash  flows from operations. At June 30, 2013, the Company had an  accumulated deficit of $&lt;font style=" FONT-SIZE: 10pt"&gt;59,398,122&lt;/font&gt;. The Company anticipates  continued losses and negative cash flows as it funds its selling  and marketing activities and research and development  programs.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  Based on the Company&amp;#8217;s current operating plan which includes  various assumptions concerning the level and timing of cash  receipts from product sales and cash outlays for operating expenses  and capital expenditures, management believes that existing cash  and cash equivalents will be sufficient to meet the Company&amp;#8217;s  working capital requirements through the next twelve months. The  Company&amp;#8217;s ability to successfully carry out its business plan  is primarily dependent upon its ability to (1) attract and retain  knowledgeable workers, (2) generate significant revenues, and (3)  if needed, obtain sufficient additional capital at acceptable  costs. The Company expects to seek additional financing and/or  strategic investments; however, there can be no assurance that any  additional financing or strategic investments will be available on  acceptable terms, if at all.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  If events or circumstances occur such that the Company does not  meet its operating plan as expected, the Company will most likely  be required to reduce certain discretionary spending, which could  have a material adverse effect on the Company&amp;#8217;s ability to  achieve its intended business objectives. No adjustments have been  made to the accompanying financial statements to reflect any of the  matters discussed above. The consolidated financial statements have  been prepared on the basis that the Company will continue as a  going concern.&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; BACKGROUND-COLOR: transparent; TEXT-INDENT: 0.25in; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  The accompanying unaudited consolidated financial statements have  been prepared in accordance with U.S. generally accepted accounting  principles (&amp;#8220;U.S. GAAP&amp;#8221;) for interim financial  information and with the instructions for Form 10-Q promulgated by  the Securities and Exchange Commission (the &amp;#8220;SEC&amp;#8221;).  Accordingly, they do not include all of the information and  footnotes required by U.S. GAAP for complete financial statements.  In the opinion of management, all adjustments (consisting of normal  recurring adjustments) considered necessary for a fair presentation  have been included. The results of operations for interim periods  are not necessarily indicative of the results that may be expected  for the fiscal year. The balances as of December 31, 2012 were  derived from our audited financial statements as of December 31,  2012. The financial statements should be read in conjunction with  the Company&amp;#8217;s audited December 31, 2011 and 2012 consolidated  financial statements and accompanying notes included in the  Company&amp;#8217;s Annual Report on Form 10-K for the fiscal year  ended December 31, 2011 and 2012 previously filed with the SEC  on&amp;#160; March 27, 2013, as amended by the 10-K/A filed with the  SEC on April&amp;#160;29, 2013.&lt;/div&gt;  &lt;/div&gt;        </NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for organization, consolidation and basis of presentation of financial statements disclosure.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -Section 50

 -Paragraph 8

 -URI http://asc.fasb.org/extlink&amp;oid=28200181&amp;loc=SL6228881-111685



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 720

 -SubTopic 15

 -URI http://asc.fasb.org/subtopic&amp;trid=2122524



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6359566&amp;loc=d3e326-107755



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6367646&amp;loc=d3e18780-107790



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -Section 45

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=7668296&amp;loc=d3e288-107754



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2197480



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 810

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=18733093&amp;loc=d3e5614-111684



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 915

 -SubTopic 235

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6472506&amp;loc=d3e38932-110933



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 852

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2209116



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 272

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6373374&amp;loc=d3e70478-108055



Reference 11: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 275

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2134480



Reference 12: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 10

 -URI http://asc.fasb.org/subtopic&amp;trid=2122150



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Organization, Operations and Basis of Accounting</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Organization, Operations and Basis of Accounting</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.responsegenetics.com/role/OrganizationOperationsAndBasisOfAccounting</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
