<?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>2401401 - Disclosure - Consolidation and Basis of Presentation (Details)</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>I2013Q2</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000074208</EntityValue><PeriodDisplayName /><PeriodType>instant</PeriodType><PeriodStartDate>2013-06-30T00:00:00</PeriodStartDate><PeriodEndDate>0001-01-01T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>number</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>pure</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>shares</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="Calendar" Id="0" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>udr_ConsolidationAndBasisOfPresentationTextualAbstract</ElementName><ElementPrefix>udr_</ElementPrefix><IsBaseElement>false</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="" 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>Consolidation And Basis Of Presentation (Textual) [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>us-gaap_PartnersCapitalAccountUnits</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>instant</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="I2013Q2" UnitID="shares"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>184281253</NumericAmount><RoundedNumericAmount>184281253</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:sharesItemType</ElementDataType><SimpleDataType>shares</SimpleDataType><ElementDefenition>The number of each class of partnership units outstanding at the balance sheet date. Units represent shares of ownership of the general, limited, and preferred partners.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 946

 -SubTopic 210

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.6-04.16(a))

 -URI http://asc.fasb.org/extlink&amp;oid=6488278&amp;loc=d3e603758-122996



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section S99

 -Paragraph 5

 -Subparagraph (SAB TOPIC 4.F)

 -URI http://asc.fasb.org/extlink&amp;oid=6959260&amp;loc=d3e187171-122770



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

 -Publisher FASB

 -Name Emerging Issues Task Force (EITF)

 -Number 87-21

 -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 AICPA

 -Name Practice Bulletin (PB)

 -Number 14

 -Paragraph 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 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 04

 -Paragraph 16

 -Subparagraph a, b

 -Article 6



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 946

 -SubTopic 210

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.6-04.16(b))

 -URI http://asc.fasb.org/extlink&amp;oid=6488278&amp;loc=d3e603758-122996



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>1</UnitID><Label>Operating Partnership outstanding units</Label></Row><Row FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>us-gaap_GeneralPartnersCapitalAccountUnitsOutstanding</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>instant</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="I2013Q2" UnitID="shares"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>174957876</NumericAmount><RoundedNumericAmount>174957876</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:sharesItemType</ElementDataType><SimpleDataType>shares</SimpleDataType><ElementDefenition>The number of general partner units outstanding.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section S99

 -Paragraph 5

 -Subparagraph (SAB TOPIC 4.F)

 -URI http://asc.fasb.org/extlink&amp;oid=6959260&amp;loc=d3e187171-122770



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

 -Publisher SEC

 -Name Staff Accounting Bulletin (SAB)

 -Number Topic 4

 -Section F



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

 -Publisher FASB

 -Name Emerging Issues Task Force (EITF)

 -Number 87-21

 -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 AICPA

 -Name Practice Bulletin (PB)

 -Number 14

 -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>1</UnitID><Label>OP units outstanding related to general partner</Label></Row><Row FlagID="0"><Id>4</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>udr_GeneralPartnersCapitalAccountUnitsOwnedPercentage</ElementName><ElementPrefix>udr_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>instant</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="I2013Q2" UnitID="number"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>true</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0.949</NumericAmount><RoundedNumericAmount>0.949</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>num:percentItemType</ElementDataType><SimpleDataType>pure</SimpleDataType><ElementDefenition>General Partners Capital Account Units Owned Percentage.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Percentage of units owned by UDR</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Consolidation and Basis of Presentation (Details)</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>NoRounding</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.udr.com/role/ConsolidationAndBasisOfPresentationDetails</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>4</NumberOfRows></InstanceReport>
