PCP/HPA : The internal temperature of a tube or tank rises during a fill. As it cools the pressure drops a little. This causes pressure to be lower minutes after than the gauge read during the fill. Use the gauge on the hand pump, compressor or fill adapter to monitor fill pressure, this is generally more accurate.
HAND PUMP : With hand pumps filling too fast or too much is not much of a concern. Pay attention to the gauge and pump at a moderate pace to avoid damaging the seals in the pump.
COMPRESSOR : Filling directly from a compressor requires a lot more care. With some you can easily fill a small tube or tank very quickly. Small PCP tubes can fill to 3000 PSI in less than 30 seconds. A large tube can fill in under a minute and a 13 cu in tank nearly as fast. Overpressurizing is the biggest risk, you could quickly end up with 4000+ PSI.
TANK : The safest way to fill from a tank is to open the bleeder, slowly open the valve until air starts to flow, then close the bleeder and let it fill slowly. You might have to adjust the tank valve a little if it isn't filling at a practical rate. It should take you at least a minute or two to fill the gun, slower than that is safer but not necessary in most cases. The maximum safe fill rate is around 50 PSI per second. This would take about 20 seconds to fill to 2000 PSI or 30 seconds for 3000. Filling too fast can cause oil or grease in the tube or tank to detonate due to rapid compression autoignition. Even silicone oils and greases can detonate if the fill rate exceeds 2000 PSI per second. Most tanks and compressors are not capable of filling this rapidly but some can. I tested how fast a scuba tank could fill a PCP gun. I was able to fill a Marauder Pistol to 3000 PSI in about three seconds and a 1701P in about two seconds.
BULK-FILL CO2 : For 22XX and dual fuel models the procedure for filling is very simple. Read these directions first, then make sure you have the gun and tank in positions where you can follow the procedure comfortably. It might be a good idea to go through the motions a few times without opening the valve so you have it all worked out before any pressure is involved.
Hold the gun with the fill nipple pointing straight up. Place one drop of oil inside the fill nipple. Keep the gun in that position as you connect the fill whip. Hold the tank in the correct position so liquid CO2, not gas, will flow out. Open the valve to blow the drop of oil into the tube. Turn the gun so the barrel is pointing straight down as it continues to fill. In that position you can fire it a few times (unloaded) to clear air out of the system so only CO2 remains. Let it fill for another minute or two, then close the valve. Some fill adapters will vent the pressure in the whip as you close the valve, some have a bleeder you need to open. When the pressure in the whip has fully vented you can disconnect it from the gun.