A paintball gun goes through many phases in order to fire a paintball. The paintball starts in the hopper, which is the paintball container on the top of the gun, and ends up in the breech. Then the paintball is hit by the bolt and is propelled through the barrel.
The role of a paintball marker is to project a paintball out of the barrel and hit another player and eliminate him. In order to project a paintball out of the marker at a fast rate of speed you need some sort of force behind the paintball. This force is applied by a high pressure air source of which it is either Co2 (most common), No2 or High Pressure air. This air is contained in tank or cartridge which is connected directly to the marker or via remote hose in some cases. All markers do not work the same way as far as the internal mechanics.
The air from the air source travels into the marker and fills a reservoir were it waits until the marker if fired. When the trigger is pulled on the marker it releases a what is called a hammer. The hammer is under pressure usually from a spring and when it is released after the trigger is pulled it springs forward and engages the valve. The valve usually consists of a piece of metal (Stainless, Brass or Aluminum) with 1 or more holes in it and down the center is a pin (stem). The stem is what closes off the valve so no air can get into it. The hammer strikes this stem forcing it open and allowing the stored air from the chamber into the valve. The air from the chamber travels thru the valve into the next section/part of the marker called the bolt, but in some markers a little air from the chamber is channeled to the hammer so it will be forced back to the cocked position so the gun can be fired again.
The valve is a cylindrical piece that has one hole at the valve area and 1 or many holes on the end (where the waiting paintball is resting). When the air travels thru the valve it enters the bolt thru the hole at the valve exit opening then travels down the bolt and slams into the waiting paintball in the breech of the marker forcing the paintball down and out the barrel and at your opposing player. That is the simplified explanation of the mechanics of how a paintball marker works, of course there are other things that are happening in each of these stages listed which is what differs in each of the different marker types. I will explain the different marker types in the Styles/Types section of this site. Below you will see an animated picture that will better show the above information that I explain, pay special attention to the blue it is the air flow. This image happens to be of a marker called the "Autococker" which is of a rather unique design but it still shows the flow of the air which is similar in most markers.
If you didn't get that, there is a more basic way to understand how a paintball gun works.
First a paintball is loaded into the marker. The compressed air goes through the hosing and makes its way into the regulator. Once the air is regulated through the regulator it is pushed into the LPR (low pressure regulator). The air is then regulated again and transfers into the bolt. The bolt then moves forward to hit the paintball. The excess air pushes the bolt back in place.