Shooting in paintball rarely resembles target practicing with a rifle. You must be able to shoot accurately while running, standing, crouching, kneeling, sitting and laying. Each position requires a slightly different technique, but with practice you can become proficient from any position on the field.
Laying on your stomach is rarely an ideal position in paintball. Unlike shooting a rifle, the stability of a front rest will not greatly increase your accuracy, so the only time you should drop to your stomach is when you are under attack or trying to stay hidden. While in the prone position, raise your upper body slightly on your elbows and hold your gun up to eye level. If you need to get lower, move your elbows farther forward which will lower your body and your gun at the same time. When you need to move, use your elbows and legs and crawl like a salamander.
The sitting position is primarily used behind bunkers. Position yourself several feet behind the bunker with your legs either straight forward or slightly to your side. Keep your gun up to eye level so you can just shoot over the top of the bunker. The sitting position utilizes the natural ability of your back and neck to shrink down and straighten out. When you straighten, you should be able to just look over the top of the bunker, shoot and then quickly shrink back into safety. Additionally, in the sitting position it is easy to lean from side to side to shoot around the bunker.
The kneeling position is similar to the sitting position, but is used when you can't see over the bunker or barrier while sitting. Position yourself on one knee, with your other leg ready to help you move. Keep your gun at eye level pulled tight into your shoulder. Raise and lower yourself primarily with your waist and back, and keep yourself only high enough to peek over the bunker. The kneeling position is also a great intermediate position when you are getting ready to run to another position.
Crouching is not comfortable and just a few minutes in the position can cause your legs to start to cramp. Ideally, crouching should only be used as an intermediate step between kneeling and standing. Keep your gun tight against your shoulder and curve your back forward to lower your profile. Keep your weight centered on the very front of your feet. When preparing to run from a crouching position, lean forward until you nearly fall and then spring into a full run rather than springing up and then running forward.
Standing is ideal for shots from a distance and while hiding behind tall bunkers. It is the most comfortable position to stay in for long periods and will be your primary position whenever you don't need to use one of the others. Keep your legs slightly bent, and spread them to a comfortable distance. If you need to lower yourself, try to spread your legs a little more rather than crouching. Hold your gun in whatever position is most comfortable, and try to keep your body as concealed as possible, exposing as little of your body as possible around a bunker.
Whatever position you are in, keep in mind what other positions you can get to if you come under fire, if you need to move or if you can't get the shot you need. Find what positions you prefer and practice them, then practice the positions you don't like as much to improve your over-all game.