Once in a while, all of us are required to quote someone quoting a third party. It's fairly easy to do as long as you remember the grammatical rules. Quotes within quotes follow the same rules for regular quotes -- only they require a single quotation mark at both the beginning and the end. The single quotation mark is generally on the same key of your typewriter or computer as the more familiar double quotation marks.
Start the first quote. Always begin with the double quotation marks as usual. When you come to the second quote, use a comma before beginning the quote within a quote. Make sure you are very clear with the names of who is saying what. Give the name of the first person who is speaking at the beginning of the first quote and then name the person he or she quotes before beginning the second quote. This example -- John said, "Mary just called and she said, -- shows you how to begin.
Start the second quote. Use a single quotation mark to begin it and punctuate it as you would a regular quote, with the period coming before you close the quotation with a second single quotation mark. Normally, a quote within a quote like this will be brief, since people usually use only short direct quotes from another person. Keep the quote within a quote as simple as you can.
Finish the quote. Often, both quotations close at the same time, so your sentence would look something like the following: John said, "Mary just called and she said, 'Something terrible has happened.'" Close the first quote and then the second, so there will be one single and one double quotation mark. If the first quote is not finished, go on to finish it: John said, "Mary just called and she said, 'Something terrible has happened.' That's all I know."
Add a third voice. Rarely, you will have someone quoting someone who is quoting yet another party. In this case, you revert to the double quotation marks for the second quote within a quote. Here is an example: John said, "Mary called and said, 'Something terrible has happened at mother's house. Mom said, "Victor's bed is empty."' That's all I know."