The Diablo III Starter Edition lets you play up to level 13. You can read about all the limitations here. You can play all of Act I up to the Skeleton King, level up to level 13, no access to auction houses (real money AH or the gold AH), and you can only be matched up to other Starter Edition players in the matchmaking system.
While this is a great way to test the game to see if it’s really as good or horrible as either side makes it out to be – it’s not an alternative to dropping $50 on the game and getting to play a gimped version (ah-la free-to-play) as much as it’s like WoW and SC2’s starter trials.
To grab the starter edition, Log in to your existing Battle.net account at www.battle.net, and sign up for the Diablo III Starter Edition through the “Your Game Accounts” section.