It's been a military fort, a notorious federal prison, an encampment for Native American activists, and the backdrop for numerous Hollywood movies. And now Alcatraz Island is a national historic site and a prime tourist attraction in the San Francisco Bay. Upon landing, you're free to wander about the island on your own. You should allow 2 or 3 hours and be aware that the pathways can be a bit steep and strenuous -- or you can take a guided tour.
If you go:
No admission is charged for Alcatraz, but you'll have to pay for a private ferry service to deliver you to the island. The ferry service also offers a combination Alcatraz-Angel Island tour that you may want to consider. The closest parking lot to the ferry is at Francisco and Kearney. Be sure to wear comfortable walking shoes and be prepared for cool weather, even in summer.
Links:

Alcatraz Cruises, LLC
Pier 33
Hornblower Alcatraz Landing
San Francisco, California 94111 USA
Mailing address:
Alcatraz Island, National Park Service
Golden Gate National Recreation Area
Fort Mason, Building 201
San Francisco, CA 94123 USA