If you sign up for the latest email updates on the Samsung Galaxy S4, you're automatically eligible to win one for free.
To win all you have to do is fill out a registration form with your name, email address, and phone number. To avoid receive any advertising materials, you should un-check the little box, I don't think there will be lots of Galaxy S4 promotional material coming your way, but that isn't necessarily a bad thing.
There are a few restrictions however, that must be pointed out and one of them is that you must be a U.S. resident in order to participate in the sweepstakes. The other is that you must be 18 or older.