As part of the tech inspection, officials will make sure there won't be anything flying around your cabin while you're on the course. You also might want to wash your car and the engine compartment if you haven't done so in months. Just before you get to the autocross site, stop at a service station and pump up your tires to 42 psi or so. It sounds high, but you will need extra air in those tires to prevent them from rolling over onto the sidewalls during hard cornering. Then let out the air until you've achieved that pressure.
Most areas have a similar procedure for participating in an event.
Ask anyone to help you if you don't have a clue. Try to ask someone that doesn't look extremely busy at the moment, and you'll probably get the most attentive assistance. Fun runs are non-competition runs, generally available at a reduced cost after all competition runs have been completed. Fun run policy varies widely from region to region as to availability, cost, passengers, and eligibility. Cars must also have passed tech .