Starting out with open track or also called HPDE events is a great way to get involved. Go to http://www.motorsportreg.com/
and click on the Event Calendar to find events in your area. NASA also puts on a great HPDE as well as TrackGuys and many others.
Be careful, its like having a cocaine habit...
I race with SCCA, but wouldn't recommend it as a starting point.
I've also done HPDE with NASA, TrackGuys and the like, and don't recommend them for the beginner.
BMWCCA is by far the best bang for your buck, head & shoulders above the rest.
Plenty of seat time, including an in car instructor, plus a structured classroom program.
They accept students with any make car, doesn't need to be a BMW.
Non-club members might get wait listed, membership is ~$50
I agree, it's a very addictive hobby...