First up, this is cycling, not football - no tackling required, thank goodness. In fact I've "tackled" this subject a few times, including right here. Crits are short, sharp races run at higher speeds than road races, usually with more corners and fewer hills, around a short course. The skill and fitness levels are high but endurance is less than a longer road race.
The essentials go a bit like this:
1. For a criterium you need a road bike. One with curvy 'dropped' handlebars and a pair of brakes will do - yes, you need to use the back brake too!
2. You need a bike with 2 lightish but stiff wheels, as flexy wheels in tight corners are not good as they feel soft and squishy and put you off
3. The bike itself could be around 8 or 9 kg in weight but extra kilos on the bike are not that much of a problem as crits are usually pretty flat. Light wheels will assist your acceleration more than a light bike. In any case you shouldn't stress about the bike. Your fitness will matter more
4. Having said that, the bike should be well maintained and unlikely to break under load!
5. Remove extraneous objects before the race - like streamers, plastic gear guards, bells, toolkits, books, magazines - and keep 'em for later
6. Pump up the tyres. 100psi sounds good but whatever you see written on the tyre will be a better guide. A harder tyre is a faster tyre, within limits (don't over-inflate as that may be dangerous, especially if the tyre blows off the rim!)
7. Join a bike club and get a racing licence. In Australia it's around $200 a year but varies with each club and your age. You get 3rd party insurance with that and a cool licence to prove you are a racer. Consider private health insurance as falling off at speed may be costly
8. Crits go round and round so you'll pass the pits several times. If you puncture (or have a 'mechanical') you will be allowed 'a lap out' but unless you are fabulously prepared and have a buddy following you with spare wheels it's unlikely you'll be able to take advantage of that in your early races. You can often leave spares at the start line anyway, just let someone know to watch 'em, in case they 'walk'. You won't get a lap out if you have reached the final lap, btw, you'll have to just watch - obey the race judge (the 'commissaire') in any case
9. Assuming you have followed my earlier advice and have trained at least enough to have sufficient endurance for the event in question, arrive at the racing venue with plenty of time in hand (30mins minimum, preferably an hour)
10. If you haven't already done so, get your licence from the club secretary. If you haven't paid, pay now.
11. If you have your licence, look for the entry desk. It could be under a marquee. It could be in a club house. There may be a queue of fit looking lycra-wearers to guide you. Queue up and pay your entry fee (could be $10 or so, more for open races). You will be graded, probably in a low grade at first. They will give you a race number (cool!) and may hold your licence untill you return said number after the race. Race numbers are often colour coded to show grade
12. Put your number on (usually pinned low on your jersey and slightly to the side where the judges sit (it pays to check out local custom here).
13. Pay attention to what's happening as races are often organised in unusual orders. Like A grade (fast guys) first, then B grade, then C and D combined, or totally in reverse. Local customs apply - don't miss your start!
14. If it's OK to do so, roll around and warm up on the course. Don't start cold in any case!
15. Don't miss the start!
16. Don't get in the way of faster grades, especially when you've finished
17. Hand your number back afterwards
18. Learn from your experience!