As far as Fontana goes, check their sched online to see when they are open to general public. Everyone tries to get there as early as possible to get the most runs in. It was $20 last time I went.
Your car has to pass a tech inspection - not a prob for newer cars but for older cars you need to make sure it's battery is tied down, radiator has a puke can, and it's not leaving oil slicks all over the track. There are some specifics like convertibles need roll bars if you are in the 13's (might be 12s - been a while). I think hard tops need a roll bar if under 11 or at least helmets? Again, check their site for rules.
They didn't want anyone running under 10s - you will be booted if you do. Some guys play the game of getting off the gas or braking to see how close they can get without being tossed... Or just go for it planning to booted. You will be issued a card for the Speedway - too many times ejected and you won't be allowed to race.
Go with a group. There is a lot of down time waiting on busy days - you may only get 3 or 4 runs in. With a group you can compare launch techniques, tire pressures, etc. Tool boxes, folding chairs, canopies, street tires if you are swapping on slicks, can be safely left with the group. And if you manage to break your car, you stand a better chance of getting home.
There are usually beer and food trucks/stands. Drivers have a wrist band prohibiting them from buying beer. Bringing food and sodas is fine - use the trash cans. Wear real shoes - no driving in flip flops .
2013 Ingot GT, 6M, FRAA Susp, GT500 Axle Backs/Wheels/Spoiler, Baer/Shelby brakes, Recaros, Trac-Cal, etc.