<?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 - Basis of Presentation and Operations</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>1</Level><ElementName>perf_BasisOfPresentationAndOperationsAbstract</ElementName><ElementPrefix>perf_</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><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>Basis of Presentation and Operations [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock</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>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" 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%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;BASIS OF PRESENTATION AND OPERATIONS&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The condensed consolidated balance sheet of Perfumania Holdings, Inc. and subsidiaries (the "Company") as of February 2, 2013, which has been derived from our audited financial statements as of and for the year ended February 2, 2013, and the accompanying unaudited condensed consolidated financial statements have been prepared in accordance with the rules and regulations of the Securities and Exchange Commission (the &amp;#8220;SEC&amp;#8221;). Certain information and note disclosures normally included in annual financial statements, prepared in accordance with accounting principles generally accepted in the United States of America (&amp;#8220;US GAAP&amp;#8221;), have been condensed or omitted pursuant to those rules and regulations. The financial information presented herein, which is not necessarily indicative of results to be expected for the full current fiscal year, reflects all adjustments which, in the opinion of management, are necessary for a fair presentation of the interim unaudited condensed consolidated financial statements. Such adjustments are of a normal, recurring nature. These condensed consolidated financial statements should be read in conjunction with the consolidated financial statements and the notes thereto included in our Annual Report on Form 10-K for the fiscal year ended February 2, 2013.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Due to the seasonality of the Company&amp;#8217;s business, with the most significant activity occurring from September through December each year, the results of operations for the twenty-six weeks ended August 3, 2013 are not necessarily indicative of results to be expected for the full fiscal year.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The Company is an independent, national, vertically integrated wholesale distributor and specialty retailer of perfumes and fragrances that conducts business through &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;color:#000000;font-style:normal;font-weight:normal;text-decoration:none;"&gt;six&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; primary operating subsidiaries; Perfumania, Inc. (&amp;#8220;Perfumania&amp;#8221;), Quality King Fragrance, Inc. (&amp;#8220;QFG&amp;#8221;), Scents of Worth, Inc. ("SOW"), Perfumania.com, Inc. (&amp;#8220;Perfumania.com&amp;#8221;), Parlux Fragrances, LLC ("Parlux") and Five Star Fragrance Company, Inc. (&amp;#8220;Five Star&amp;#8221;). See Note 2 for discussion on the acquisition of Parlux. We operate in &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; industry segments, wholesale distribution and specialty retail sales of designer fragrances and related products.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Our wholesale businesses include QFG, Five Star and Parlux.  QFG distributes designer fragrances to mass market retailers, drug and other chain stores, retail wholesale clubs, traditional wholesalers, and other distributors throughout the United States. It sells principally to retailers such as Walmart, Kohl's, Nordstrom Rack, Marshall's, Target and Ross Stores. The Company&amp;#8217;s manufacturing divisions, Parlux and Five Star, own and license designer and other fragrance brands that are sold to regional and national department stores, international distributors, through QFG, SOW&amp;#8217;s consignment business and Perfumania&amp;#8217;s retail stores, paying royalties to the licensors based on a percentage of sales. All manufacturing operations are outsourced to third-party manufacturers. &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Our retail business is conducted through the following subsidiaries:&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-left:48px;padding-top:6px;text-align:left;text-indent:30px;"&gt;&lt;font style="padding-top:6px;text-align:left;font-family:inherit;font-size:10pt;padding-right:18px;"&gt;&amp;#8226;&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Perfumania, a specialty retailer of fragrances and related products,&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-left:48px;padding-top:6px;text-align:left;text-indent:30px;"&gt;&lt;font style="padding-top:6px;text-align:left;font-family:inherit;font-size:10pt;padding-right:18px;"&gt;&amp;#8226;&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;SOW, which sells fragrances in retail stores on a consignment basis, and&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-left:48px;padding-top:6px;text-align:left;text-indent:30px;"&gt;&lt;font style="padding-top:6px;text-align:left;font-family:inherit;font-size:10pt;padding-right:18px;"&gt;&amp;#8226;&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Perfumania.com, an Internet retailer of fragrances and other specialty items.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;As of August 3, 2013, Perfumania operated a chain of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;334&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; retail stores specializing in the sale of fragrances and related products at discounted prices up to &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;75%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; below the manufacturers&amp;#8217; suggested retail prices. Perfumania.com offers a selection of our more popular products for sale over the Internet and serves as an alternative shopping experience to the Perfumania retail stores. SOW operates the largest national designer fragrance consignment program, with contractual relationships to sell products on a consignment basis in approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2,400&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; stores, including approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;1,200&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; Kmart locations nationwide. Its other retail customers include Burlington Coat Factory, Loehmann&amp;#8217;s, Steinmart and K &amp;amp; G.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:12px;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&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 the basis of presentation and significant accounting policies concepts. Basis of presentation describes the underlying basis used to prepare the financial statements (for example, US Generally Accepted Accounting Principles, Other Comprehensive Basis of Accounting, IFRS).  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