Ok so playing with this for the past few hours I've come to these conclusions: (This is as of NOW)
Use this link: http://store.origin.com/?ipr=ty
Use this code: OS3874XVC
You can get 3 free games per account.
You must add the game to your cart before logging in.
When you get to the final page after hitting checkout, just log in however.
You need to clear your cache/cookies after each purchase, or use an incognito browser tab like Chrome.
If it doesn't work, you either got your 3 games, or you didn't flush your cookies/cache.
I've tried multiple accounts, multiple login techniques, and I have yet to get a 4th free on a single account, but I have managed to get exactly 3 every time without much effort following those steps.
Late last night around midnight, many people were able to checkout multiple games at once, making the "3 game per account" not true. This has been fixed, as the code only takes the price off a single game when applied to a cart.