In British English a normal quotation uses the single quotation mark.
John said he was 'tired and hungry' and would go straight to bed.
In American English a normal quotation uses the double quotation mark.
John said he was "tired and hungry" and would go straight to bed.
For quotes inside quotes, British uses the double quotation marks and American the single.
British:
John said, 'Jane told me she was "tired and hungry" and would go straight to bed'.
American:
John said, "Jane told me she was 'tired and hungry' and would go straight to bed."