Correctly balancing your rc airplanes is so important for safe flying, because any deviation from the model's Center of Gravity (CG) can and probably will result in the model being quite uncontrollable.
Every rc airplane has a correct CG, this is the point where the model balances fore-aft correctly. If you've built from a plan, then the CG will be marked on the plan. If you've bought an ARF or RTF plane, then the manufacturer's instruction manual should tell you where the CG lies for that particular model.
A very badly balanced rc plane will, at best, be hard to control, and this is especially true for tail-heavy planes. At worst, the plane will crash within seconds of getting airborne!
High wing trainers are the easiest airplanes to balance, and if it's your first plane then this is likely to be the case.
Obviously the first thing you need to do is identify the correct Centre of Gravity, according to the plan or manual. As a general rule of thumb, the CG will be about one-third of the wing chord (width) back from the leading edge of the wing.
Place the tips of your index fingers, or middle fingers, under each wing, on the line of the CG. A couple of inches out from the fuselage is a good point. Gently lift the airplane up so it is clear of any surface, and let it hang freely on your fingers.
A correctly balanced airplane will either be level, or with the nose pointing slightly downwards. If the tail points downwards, then the model is tail heavy and you need to do something about it.

If the balance does need to be adjusted, the first thing to do is try moving any of the rc gear either further forward or further back inside the plane. By doing this, you are adjusting the balance without adding extra weight to the model, in the form of ballast.
The battery pack is the best thing to try and move, because it is the heaviest and so will have the most effect. Carefully try and reposition it, always rechecking the balance of the plane every time you move it. Once you're happy with the new balance, make sure that the battery pack always stays in its new position.
If you can't reposition anything, which is often the case in RTF airplanes, you might have to add ballast to either the nose or the tail of the plane. You need to remember, though, that ballast adds dead weight to a model - the lighter a plane is, the better it performs. So if you do need to add ballast to correct the CG, you need to add as little as possible.
The way to do this is to add the ballast as far forward or as far back as you possibly can, on the model. By doing this, the ballast will have the most effect on the CG. Add only enough to make your plane balance correctly on your fingertips.
This is an often overlooked balance, and in many ways isn't particularly important. But an rc airplane that has one side heavier than the other, will have a tendancy to naturally roll and turn to the heavier side, making your life a bit harder.
However, roll balancing isn't nearly as important as fore-aft balancing talked about above. Unless something is seriously wrong, the plane won't spiral out of control just because one wing is slightly heavier than the other!
To balance your airplane's roll, simple loop some thread around the propeller shaft, between the spinner and the fuselage, and then some around the rear of the fuselage, as close to the tail as you can get.
Lift the plane up and let it hang freely - see if it wants to roll to one side or another. If it does, then you need to add some small ballest to the wingtip of the lighter (higher) side. Add only enough to make the plane hang level, when viewed from the front. Taping the weights to the wingtip is an easy method, although you might want to take the trouble to set them into the wingtip, then cover over them to hide them.

So there you have it... two methods of balancing rc airplanes. As already mentioned, the fore-aft balance is fairly critical if you want to keep your plane in one piece; the roll balance isn't so critical but is worth doing if you have the time.
A correctly balanced plane will always be safer and easier to fly, and won't need as much trimming at the transmitter.
Ground school - the basic stuff that you should know before you start flying model planes.
Flying model airplanes - 1st flight tips for a basic model.
RC airplane controls - the primary ones and what they do.
RC flying do's and don'ts - some basic safety tips.