<?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>2101100 - Disclosure - Business and Basis of Presentation</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>D2013Q4YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001045829</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-07-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="12 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="D2013Q4YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;BUSINESS AND BASIS OF PRESENTATION&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Reporting Entity&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Vanguard Health Systems, Inc. (the &amp;#8220;Company&amp;#8221;) is an investor-owned health care company whose subsidiaries and affiliates own and operate hospitals and related health care businesses in urban and suburban areas.  The Company's common stock is traded on the New York Stock Exchange (symbol "VHS").  As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company&amp;#8217;s subsidiaries and affiliates owned and operated &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;28&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; acute care hospitals with &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;7,081&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; licensed beds and related outpatient service locations complementary to the hospitals providing health care services in San Antonio, Harlingen and Brownsville, Texas; metropolitan Detroit, Michigan; metropolitan Phoenix, Arizona; metropolitan Chicago, Illinois; and Massachusetts. The Company also owns managed health plans in Chicago, Illinois; Detroit, Michigan; Harlingen, Texas; and Phoenix, Arizona, and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;two&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; surgery centers in Orange County, California. &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Recent Developments&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On June 24, 2013, the Company announced that it has entered into a merger agreement with Tenet Healthcare Corporation (&amp;#8220;Tenet&amp;#8221;). Pursuant to the merger agreement, each of the Company's common shares will be converted into the right to receive $&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;21.00&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; per common share in cash and Tenet will assume the Company's net debt. The Company will become a wholly-owned subsidiary of Tenet and the Company's shares will cease to be traded on the New York Stock Exchange. The merger is subject to customary regulatory approvals and specific obligations that are required by parties to become effective. During the year ended June 30, 2013, the Company recorded $&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;7.8 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of transaction costs related to the merger that is included in acquisition related expenses on the accompanying consolidated statements of operations. The transaction is expected to close early in the Company's second quarter of fiscal 2014. &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Basis of Presentation&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The accompanying consolidated financial statements include the accounts of subsidiaries and affiliates controlled by the Company. The Company generally defines control as the ownership of the majority of an entity&amp;#8217;s voting interests. The Company also consolidates any entities for which it receives the majority of the entity&amp;#8217;s expected returns or is at risk for the majority of the entity&amp;#8217;s expected losses based upon its investment or financial interest in the entity. All material intercompany accounts and transactions have been eliminated. The share and earnings per share information included in the accompanying consolidated financial statements and included in Note 10 reflect the impact of the stock split that the Company effectuated in connection with the initial public offering of its common stock in June 2011. The majority of the Company&amp;#8217;s expenses are &amp;#8220;cost of revenue&amp;#8221; items. Costs that could be classified as general and administrative include certain corporate office costs of the Company, which approximated $&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;73.1 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, $&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;67.8 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and $&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;62.4 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the years ended June&amp;#160;30, &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2011&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, respectively.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Reclassifications&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Certain balances in the accompanying consolidated financial statements and these notes have been adjusted to conform to the June 30, 2013 presentations.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Use of Estimates&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:13px;text-align:left;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In preparing the Company&amp;#8217;s financial statements in conformity with accounting principles generally accepted in the United States, management makes estimates and assumptions that affect the amounts recorded or classification of items in the consolidated financial statements and accompanying notes. Actual results could differ from those estimates.&lt;/font&gt;&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 FASB Interpretation (FIN)

 -Number 46R

 -Paragraph 4, 14, 15

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 2: 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 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name FASB Staff Position (FSP)

 -Number FAS140-4/FIN46(R)-8

 -Paragraph 8, C1, C7

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 4: 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



Reference 5: 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 6: 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=7880789&amp;loc=SL6228881-111685



Reference 7: 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 8: 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 9: 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 10: 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 11: 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 12: http://www.xbrl.org/2003/role/presentationRef

 -Publisher AICPA

 -Name Accounting Research Bulletin (ARB)

 -Number 51

 -Paragraph 2-6

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 13: 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 14: 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 15: 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 16: http://www.xbrl.org/2003/role/presentationRef

 -Publisher AICPA

 -Name Statement of Position (SOP)

 -Number 94-6

 -Paragraph 10

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>BUSINESS AND BASIS OF PRESENTATION</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Business and Basis of Presentation</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.vanguardhealth.com/role/BusinessAndBasisOfPresentation</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
