The only way to get a "free" Xbox Live account is to make a silver account. But you will not have access to many of the features that gold members recieve, especially playing online and the Live Marketplace.
There truly isn't a way to get a free Gold Live memberships. Unless you have friends who have Live trial codes in some other their games. Halo, Call of Duty, and Gears of War are the best Xbox titles to check for codes (used copies obviously. Used copies will most likely not have the code in them). Almost every Halo title has a trial code, and Halo 4 has a 14-day gold trial code in the box.