Answer:
Freedom for: To gain freedom for someone or something who is being enslaved or controlled, to deliver freedom to someone or something who's not free, to make someone or something free. Example: During the American Revolution, the patriots were fighting to gain freedom for the American people (or for the United States).
Freedom from: To be free from someone or something which is the source of oppression or control. Example: During the American Revolution, the patriots were fighting to gain freedom from Great Britain.