Try this link for online Alcatraz ticket purchases:
I used this a couple of years ago when relatives came into town, and it saved so much time. You specify the date and a block of time you're willing to go -- then you pick up tickets at the "Will Call" window right by Pier 41. There is a surcharge to order online, but trust me, it's worth it.
Otherwise there's a high probability you can't score tickets at all. That's prime tourist season and everybody wants to go to Alcatraz.
PS Go ahead and spring for the audio tour. It makes it much more interesting.