A few notes about game mechanics:
The basic mechanic is 1d20 vs a target number, usually a skill level. Rolls equal to the target number or lower mean success. Higher means failure, so rolling low is good. The degree of success or failure is also important. If your Demolitions skill is 8 and you roll an 8, you are successful in setting that charge but it may not cause as much destruction as you'd hoped. A 3 or 4 means things went much more as planned, whereas if you roll a 20... well, they're probably prepping that fresh clone as we speak.
To make things interesting (this is PARANOIA, after all), each player gets a pool of Perversity points. These are awarded at the beginning of play and also when you, the player, make things more fun. And by fun, I mean keep things interesting, lighthearted, exciting, and deadly (but only in a stylish way

). Perversity points can be spent to adjust a target number.
Any player's target number, not just your own. You must provide some narrative reason for this modifier ("I know it looked like an easy shot, but you just hit your head on a piece of low-hanging conduit and that threw off your aim. I'm spending 5 Perversity points to give Fred-R-BKZ a -5 to hit.")
Damage calculations are based on degree of success and statistics from the weapon in question. This will become clearer during play. There are 7 level of health (or lack thereof): Ok, Snafued (stunned/distracted), Wounded, Maimed, Down (mostly incapacitated; you may be a bloody mess but you can still say a few words, hear your soon-to-be-killer gloating, pull the pin on a grenade, etc), Killed, and Vaporized (usually meaning killed with style.) Troubleshooters are outfitted with laser pistols and reflec armor which is only (somewhat) effective against laser weapons (and only the kind of laser weapons that RED Clearance Citizens are allowed to have.) Laser pistols have replaceable barrels, each containing 6 shots.