Use prime marks for measurements (single prime for feet, double prime for inches).
Use curly quotes for quotations
Use a curly apostrophe (backwards C shape) for contractions, regardless of where in the word the missing letters fall.
Use curly single quotes (open and closed apostrophes) for quotes within quotes.
In American English, virtually all punctuation marks fall within the quotation marks; in British English, the only punctuation marks that fall within quotation marks are those that occur in the original material being quoted. The American standard seems gradually to be giving way to the more rational British one.