The guns are fairly accurate up to 125 feet. Some are more so than others, and some seem even more so when in reality it's the player who's a more accurate shooter.
Check out how accurate your gun is by shooting a few shots over by the chrono station. AIM. This is very important for getting off good shots!
The two techniques used by a lot of players are to aim using sights or down the barrel, and to aim by following the stream of paintballs as you shoot them out.
The first technique is hampered by the inherent inaccuracy of paintballs. With good paint you can expect about a 25% deviation if not more. With mediocre paint you can expect a lot of variance in accuracy. In such cases, you are forced to rely on visually walking the balls onto the target as you shoot.
This method works well in that it puts a lot of paint out there and that increases the chances of hitting the opposition. It's bad in that it wastes a lot of paint and it alerts the target as to their situation, allowing them to tuck in behind their cover more securely.
You will likely end up using both methods, but try and aim once in a while cuz it actually is the better of the two methods.

Standing- Put your left foot forwards, put your gun to your shoulder using the bottle or stock as a shoulder stock. With your left hand hold the barrel or foregrip firmly. With your right using your middle finger, pull the trigger. This is the basic stance, to make it better, turn your body so that your left shoulder comes forwards and your right falls in line. This presents a thinner target to an opponent. Tuck your right elbow down close to the bottle and your body.
Sight over the barrel or down the side of the barrel. Hold the gun firmly. Holding it firmly will increase your stability and therefore the accuracy of your shooting.

Laying Down- Laying down presents a lower profile, and if there's any growth or underbrush, it can be very good for hiding and obviously allows for crawling.
It also inhibits quick movement, and if you're not in undergrowth you may find laying down to be the wrong position to be in. If you're walking along and someone surprises you and you're
not hit, fall to the ground BACKWARDS, this allows you to see what's going on adn maybe bring your gun to bear on the ambusher. This position is also good if you're in a tight place but need to be ready for immediate action. By laying on your back you can present a low profile, but be able to rise to shooting position very quickly, as well as roll off to one side or the other mcuh easier than on your stomach. On your stomach to get the same amount of range of vision, you must bring your head up higher and in a more awkward position.

Kneeling- Kneeling is sometimes best on both knees. This gives your upper body more freedom of movement than on one knee. It also let's you get lower faster, whereas on one knee you are restricted by the up knee's height. Movement, however is a little more restricted. Try different stances beforehand to see what's comfortable and to get the body used to the idea.

A clean barrel is more likely to shoot straight than a dirty one. Depending on the paint and other things, you may find your gun is breaking a lot of paint in the barrel. This can be a terrible thing for a player. Bad Paint is perhaps the very worst of all things that can befall you while playing ball. If you find you're having a lot of ball breaks inside the gun, be sure and mention it to someone and they will hopefully give you a squeegee and a lesson on how to use one. Squeegees come in two basic forms, a stick squeegee which is a long rigid stick that has a rubber disk on one end. The rubber disk folds over when you hold the other end of the squeegee in, then you slide the disk into the barrel (by folding it down, you don't push the gloppy paint back into the barrel) when you reach the end, you release the far end, and the disk folds back and you pull it out the front. It will effectively remove most of the gack. You can do it again to help clean it more, than often the front end has a bit of rag attached to it and you can run it through to further wipe out the goo. The second type of squeegee is a Jerk-Pull through Squeegee. most Jerk Squeegees are on a cable with 4 or 5 rubber disks followed by a rag or a bore cleaner. This requires removal of the barrel, then you run it through. This cleans the barrel absolutely. If your Barrel has porting at the end (which makes the gun quieter) you may have to dry-fire to clear out the porting. This is trickier because you have to cap off the end so that the air of a dryfire shot pushes out the paint in the porting. You must be sure that no paint feeds into the gun when you do this, or you will either break another ball in the barrel or shoot a ball into your hand...
If you're comfortable with the guns, learn how to clean your barrel as soon as possible. You can tell that you're breaking balls if as you shoot you see spray come out the barrel end.
Too much ball breakage in the barrel can actually clog your gun, so don't let it get too bad. Also if you break a ball and it get's into the hopper, you will coat the balls in the hopper with paint and
will likely break more paint or certainly experience lousy accuracy. If your balls are flying curley-ques, it's a possible sign that you have broken some paint.
In the Staging Area take a look inside the hopper and check. If the paint is broken, dump it out into a paper towel (30 rounds or so at a time,) wipe them down and put them into another papertowel or loader. Continue until you clean out all the paint, and then clean out the inside of the hopper and anywhere else you see gack.
You can do this on-field, and if you find you've got bad paint, bring some paper towels onto the field.

The thing we see most when we're scanning the field for the opposition, is movement. The head is actually the biggest mover, as it can crane about 180 degrees. That's what you look for, goggles moving.
Likewise, though, you should learn to hold your own head movement down to a minimum. When you move through the woods, move as gracefully as you can, and as low as you can. From the other side of the field, a player may not see you move if you're bent over even a little. Sometimes it's best to move fast, other times slowly. You'll have to figure that out on the day.
In general you can't outrun a paintball. It's going 299 feet per second, and within 125 feet, it's probably going to catch you. However, it does take time to aim and fire at someone. Then it does take time for the ball to travel to you. So if you run across from one tree to another that's 10 feet away, and the shooter is 100 feet away and isn't shooting at you yet, you can probably make the move. Figure it like this, it takes a half second to pull the gun up, a half second to aim and shoot and a quarter second for the ball to get to where it's being shot at. That can be up to a second and a quarter, and you can certainly move faster than that.

Look and see where you're moving to before moving. If you're moving out of cover into the great unknown, look around and note what will suffice as cover if you get ambushed. Put the cover between you and them. If you come under fire, and go to cover, don't go to cover in a half ass way. Take cover and get into a position where you can fight from deep cover if you have to, then check out the situation.
Taking a peek- When you take a peek, use your head, but try and keep your body behind cover. be ready to whip your head back, you may have that second and a quarter, you may not!
When you become more experienced, you can try training your body to move quickly. The trick is stand about 15 feet from a mirror, step to where you can't see yourself, get in a shooting posture, now lean over so you can see yourself in the mirror. When you see yourself, immediately pull back your body to go. Doing this will train your body HOW to do it, so that when you are in the field you can react to the situation immediately rather than having to tell your body to get under cover. It works. An advanced trick to this is to do it with a gun in hand and get off a trigger pull before moving back. You can do it without a gun, by just pretending.
You can also do this kneeling down, and from the left and right.

Choose where you'll retreat to before pulling back. Don't give up too much turf when you pull back, as it may expose your teammates by opening up their flanks.
Sometimes moving back a little works well, especially if your position is under heavy or accurate fire. Moving to a new position may give you a better shooting lane, or force the opposition to move to
a less advantageous position. Be ready for them to move up when you move back, you may well catch them in the middle of a move without much cover!

Consider a tree as cover. It may be a big tree, and to the front it presents a solid place to stand and fight behind. But if you can get to the side somehow, you will effectively make the cover smaller. So when you're attacking someone, think about how to get a better angle on their position.
This is called Flanking. The best kind of flanking move is one where the opposition doesn't know you've made the move. This way when you come out to shoot at them, they may not have moved their position to protect them from your new position. To do this kind of move, you have to wait until they are not looking at your position.
You can encourage them to duck by shooting at them, when they duck immediately move to a new position. (You should always be prelocating your next position!) If you have help, you can make the move without worrying as much that they see you since your partner should be forcing the other side as well, making the tree very very lousy cover!

If you're hiding behind a tree, the closer you get to it the more you have to expose yourself when you look around the tree. If you back off the tree a little you can look around the tree while exposing yourself less. This works both ways though, and you should be ready to hug that tree if you come under fire! This works with all manner of cover.