As noted, it varies by track.
Often the rules are not even known prior to the drivers meeting and even than can sometimes be vague or applied differently. Rules have never posted in writing at the 5 races I've been at (to the best of my knowledge).
First rule: Always be safe. Gas is serious stuff.
At NL the rule was you must fuel in the hot pit lane, max of 3 team members over the wall, all must be in full nomex, with helmet and visor, one must be holding a fire extinguisher, and the driver cannot be in the car, car must be off and no any other work being done while fueling. Overflow spills discouraged and fuelers were expected to immediately clean up. No catch trays for spills available.
After fueling, a driver change is done. Jay clarified during the race that a driver only change (e.g., no fuel) was not permitted on pit lane (although a 1/2 hour earlier a Lemons staff member in HQ said it was). There was confusion (e.g., inconsistent messages / enforcement by the safety crew) over whether cracking your helmet visor was acceptable (since fogging and thus being able to see during fueling was a serious issue).
No more than 40 gals in the paddock was written in forums but never stated during the driver's meeting to the best of my recollection. NL had campfires all around so hauling fuel jugs around (in an unstable wagon) was dicely. We never had a reason to fuel in the paddock (and I hope others were not!).
Similar hot pit lane rules at CMP but no rule on not having car running. Fueling was permitted in paddock spaces (but be aware of smoking and welding, etc. concerns) at fall race but I don't think it was allowed in the spring. Fuel spill trays were provided in pits and spills were to be dumped in catch cans. No penalty for small spills caught in trays. Driver only (no fuel) changes were permitted in pit lane at CMP but no other work on the car.
No pit lane at Stafford CT. A designated area in the pits was the only area where fueling was permitted. Driver out of car/car off. New driver could belt up within the fuel area after refueling occurred.
-- John Robertson / Schumacher Taxi Service
Know more about a Craptation, coROLLa and BMW than I ever wanted to!
Stafford 08, CMP Spring/Fall 09, Stafford 09, Nelson Ledges 09, CMP Winter 10, VIR Chump 10, IOE Winning Craptation CMP Spring 2010, and lots more