There will probably be more classes at Encino over the winter-- send an email to Ken Avchen (his email address is available on the Encino site).
Do you have much cycling experience already? If you're a pretty experienced road or mtn bike racer you might be able to take the accelerated class at ADT, which is offered almost every saturday. If you're pretty new to cycling and racing there's also a more expensive but more thorough class at ADT that's offered less often. Check the link in my sig for the schedule. ADT also offers a "First Ride" for $15 so you can get a taste. It's by appointment and it doesn't get you cleared to ride the track any other time, but it does give you a feel for riding a world class track in a pretty controlled environment-- you'll get a nearly empty track.
Encino generally wants you to ride the wednesday night open training a few times before you start doing the tuesday practice races. At ADT once you're cleared to ride you're good for most things except for Elite training time (different levels of rider ride on different parts of the track during non-elite structured training). For both you should have a USCF license (available at http://usacycling.org
- you want the USCF license only. You might also want to wait until the new year to get one because they're good Jan 1 to Dec 31-- you can probably take classes before then.
Track rules you learn in the classes (and there are slight differences between the rules at the two tracks, as well as San Diego). The rules for racing are in the rulebooks that you can download from the USACycling site.
Decent track bikes can be gotten new or used for $500 or less, though you'll start accumulating things like tools, cogs, and chainrings that will increase the outlay. All tracks have rentals that you can use for open riding and training, but generally not for racing.
I got into track cycling when I was doing a lot of recreational rides in Minnesota with the AYH bike club. A few of the people in the club also were in a racing club, and raced on the track, and they organized a "Get High On the Track" session that included bike rental and track time for $5-- the Minnesota track is a lot like ADT but outdoors and the banking is pretty high. It was a blast and my girlfriend and I signed up for the 4 session class to get cleared to ride for training and racing ($50). I think we took the class in the fall, and she bought a track bike over the winter, and I got one in the spring.
It's very addicting-- the racing is really intense and fast paced (I find it much more fun than road or crits), and training can be really hard or really relaxing, depending on what you're doing. Track skills translate well to the road, but road doesn't translate as well back. I was doing ~100 miles/week on the track much of this year (plus road miles), including racing just about every weekend at either Encino or ADT.
One thing that a lot of people don't realize is that there are track races for all different sorts of rider-- it's very much not just about sprinting. The shortest events are the sprints, but points races can go 30-40 km at pretty high intensity and demand a lot of endurance.