As I understand it, the MLS is a closed league and every player's registrations are held by the MLS itself. The club bids for player contracts and there is a draft every year which distributes college players to the MLS clubs. There is a salary cap, but there is also a special player exception, which allows players like Beckham, Xavier, Angel, Donovan etc to recieve a higher wage than the others (I think it's 3 allowed per club).
The top 4 teams in the western and eastern conferences face each other in play-offs and the winner of these is the overall MLS winner. There is also the open cup, which I imagine to be their equivalent of the FA cup.
There are other leagues in the US though, such as the USL which has Stoke City's sister team, the Austin Aztex.