You need to sign up through the clubs. You might find some you can get into though Motorsportreg.com but generally you will need to become a club member for a nominal fee. The clubs are usually regional so try and find the ones in your area. If you have a track close by and you really get the bug you can get a track membership, but those tend to be rather expensive.
Just some clubs off the top of my head that will let anyone join.
COM
SCMC
SCCA
BMW
They usually divide the running into experience groups, Novice, Intermediate, Experienced. You will have to sign up as a Novice at first and will have an instructor riding with you. Instructors are usually great and help you get comfortable with the track and the correct driving line.
A lot of clubs are having trouble filling the registration sheets at the moment so you might be able to get into some events on fairly short notice. Once you get the bug you'll be driving to all the tracks in a 500 mile range
