You use the same kind of quotation mark as you would for anything else. So British English will standardly use the single quote and American English will standardly use the double quote.
Just remember that when you use quotes within already quoted material, you switch which quote you are using. Some examples:
British English:
• Sally frequently confuses the words ‘literally’ and ‘figuratively’ when speaking.
• ‘Sally frequently confuses the words “literally” and “figuratively” when speaking’, James said.
American English
• Sally frequently confuses the words “literally” and “figuratively” when speaking.
• “Sally frequently confuses the words ‘literally’ and ‘figuratively’ when speaking,” James said.