The use of single or double quotation marks is a matter of preference – both are correct. I prefer single as I think the text looks cleaner and easier to read.
- ‘Where is the toilet?’ he asked the waiter.
- “Where is the toilet?” he asked the waiter.
For quotations within quotations use the opposite to what you normally use.
If you normally use single quotation marks:
- ‘Did he really say, “I hate you” to his mother?’
If you normally use double quotation marks:
- “Did he really say, ‘I hate you’ to his mother?”