What are some good ways school kids can get started with chess in the San Francisco Bay Area?
The San Francisco Bay Area offers a variety of learning opportunities for chess enthusiasts. You could attend classes in-person or online, attend drop-in clubs in-school or after-school, and play unrated or rated chess tournaments.

Here are some suggestions:
1. Watch introductory chess videos from chesskid.com. It offers both free and paid memberships.
2. Buy introductory chess books and work through graded chess puzzles. 
3. Attend some chess clubs and play games. 
4. Play in an unrated tournament and then in USCF rated scholastic chess tournaments. 

One such organization is Bay Area Chess, which offers chess events all over the Bay Area.