I will be going to the velodrome soon myself for the first time ever so your advice and experience is most welcomed.
The two main points I would make are these; the instruction is very good and for me it's been a great experience. I could easily get hooked.
My son bought me three sessions for Father's Day and I've now done two. At the first we were given a full introduction to the bikes, track safety and how to use and ride the track safely. The majority of riders, as per the instructors guidance, only went halfway up the track. I went to the top and got a quiet thumbs up from the instructor.
My sessions have been 12.00 - 1.00 and there have only been 6-8 riders on the track at anytime. The experience and/or ability of the riders varies considerably.
After my first session the coach quietly said to me "you can clearly ride a bike. Next time I'll show you how to ride on a wheel." This we did yesterday and it's a great experience, really good fun.
I crashed yesterday because I slowed on the curve. I don't know if I was warned against this or not. Basically the way to stop is to gently slow and drop on to the narrow light blue strip which is used to get up to track speed. Then one moves across to the wide dark blue area to ease off and roll to a stop. For some reason when slowing I stayed about 4/5 feet up the curve, didn't have enough speed to maintain traction and the wheels simply slid away from me.
The above apart the only possible ways I can see to crash are contact with another bike, contact with the top wall or stopping pedalling at speed!!
Unless you want me to I don't think I should comment on what one is taught as this is what the, very good, instructors are there for. I'm sure you'll learn a great deal, begin to understand how the track construction aids the riding and above all will have a great time.
Just remember the Velodrome is behind the big ASDA, it's not easy to spot.