Single quotation marks can be tricky to understand because they are often used incorrectly. Many writers use them improperly for effect, and in Britain, they are sometimes used in place of regular quotation marks. In the U.S., there is only one correct use of single quotation marks: to set off a quote within a quote.
Look through the source information you are planning to quote. Has that author quoted someone else? If so, this is a good time to use single quotation marks. In this instance, you want to quote the author and whomever he or she has quoted. So you have a quote within a quote.
Use the apostrophe key to type single quotation marks.
Place a single quotation mark immediately before and after the quote within a quote. But remember that the regular quotation marks must also begin and end. For example: "Mary told her sister 'you look cute' on Halloween," she wrote. This can get a little jumbled when the quote within a quote begins or ends the full quote. For example: "'You look cute,' Mary told her sister on Halloween," she wrote.
Place all punctuation inside quotation marks. This goes for single and regular quotation marks. Notice the placement of comas in Step 4.