Use single quotation marks for a quotation or title using quotation marks inside another quotation or title which uses quotation marks.
Incorrect: She asked, "How many of you have read "The Lady of Shalott"?"
("The Lady of Shalott" is a poem. Same kind of quotation mark confuses reader.)
Correct: She asked, "How many of you have read 'The Lady of Shalott'?"
For titles or quotations within quotations within quotations (and so ad infinitum), alternate double and single quotation marks.
Example: Helen said,"She asked us,'How many of you have read "The Lady of Shalott"?' I had."
(The most this author has seen is five levels of quotations in Lord Jim and Heart of Darkness by Joseph Conrad and The Metamorphoses by Ovid.)
Note: In the British Isles the use of the single and double quotation marks is reversed from the way they are used in the United States. There the normal quotations and short titles are within single quotation marks. Double quotation marks are used for titles or quotations within quotation marks.