Gas systems can be divided into a couple categories:
Blowback: Straight blowback is generally not suitable for rifle rounds because bolt has to be excessively heavy. It simply works with an unlocked breach. When the gun fires, the bullet goes one way, while the casing (and bolt) go the other. The weight of the bolt is balanced against how powerful the cartridge is, more power = heavier bolt needed. Adding a delay mechanism of some sort allows the design to be used for the more powerful stuff. (HK G3[roller-locked delayed blowback])
Long stroke gas piston: This is generally a gas port in the barrel which leads to a gas cylinder. A piston in the cylinder is pushed backward by gas pressure when the gun is fired. This piston operates the locking mechanism by some mechanical linkage, and generally moves the same distance that the bolt/bolt-carrier/whatever moves. (AK and M1/M14)
Short stroke gas piston: This is generally the same as a long stroke, except the piston does not move the full distance that the action does. It uses a larger piston and/or gas port so that a much larger force is applied to the piston. However, the piston transfers this force to the action over a very short distance, at which point the piston stops and the action keeps going under its own momentum. Essentially the piston 'flings' the action backward but moves very little itself. (Dragunov, FAL, SCAR, G36)
Direct Impingement: In this system, gas is vented directly from the barrel, through a passage way, and directly against the bolt-carrier/whatever. This applies force to the action without any sort of piston/cylinder assembly involved. Stuff tends to get fouled more quickly, but it keeps everything a little bit simpler and lighter weight. (M16/AR15)
As for recoil operation, theres a bunch of different designs and someone else can address them.
P.S. I found these two pages while double checking myself.
http://www.answers.com/topic/firearm-action
http://matrix.dumpshock.com/raygun/basics/operation.html
(and don't read the wikipedia page, its wrong)
