Check out
www.nasaproracing.com. They are a good place to get started running around a track. There are several other groups in Cali (trackracers, etc.).
I run SCCA for road racing. It is a bit expensive to get started in (car + schools + safety gear + physical, etc). NASA is much easier.
Just look for driving schools and lapping events. It should be about $300 for a weekend and in NASA that's several hours of track time. For HPDE events, you don't normally need more than an approved helmet.
Once you go to a few lapping/school events, you can decide whether to step up to full competition. For that, you'll need to choose an organization and class to run in. Everything has rules to follow that limit you on preparation, etc.
To go roadcing where you can pass anywhere on the track, you'll need a competition license, a car with a cage and other safety equip (see rules), a nomex suit, SA2000 helmet, etc. It's a blast.
Email me for any questions
grover@nissport.com
Grover
http://www.nissport.com
