A competition is a fight between two persons, and can be won in several ways. The rules for WTF Tae Kwon Do can be found below.
A point is made by a successful fist-punch in the centre of the opponents body. A successful attack with the foot onto the head, or the centre of the opponents body also results in a point. If the opponent falls down after a legitimate kick or punch: a point. This doesn't mean that it is easy to make a point. Usually a few points (i.e. about three) are made in a competition (usually three rounds of two minutes...).
The rules in a (W.T.F.) competition are very easy: It is not allowed to kick below the belt. On the other side, almost any kick above it is allowed. Only exceptions are: You may not kick your opponent in the back and not at the back of his/her head. If you kick someone in the back while the other is turning, it is not really your fault, so usually the fight will continue without any points.... It may result in negative points for you, however. Punches may me given, but only on the body, not on the head. It may sound like these rules leaves almost no place to kick, but this is not true. You can win on a K.O. and lots of kicks are directed to the head. You have to be quite fast to avoid these kicks, and react with a (better) kick.