To enter these kind of competitions you obviously need to play a game. Games can be casino related, similar to computer games or even just an interactive style quiz. To enter, you may need to get a high score, pass a certain level, get the overall high score, play against and/or refer a friend, or accumulate points for prize draw entries.
You may require Shockwave to take part in these kind of competitions. Some game sites make use of Java - this works automatically on many of the latest browsers, however people accessing these sites through via a corporate firewall may experience problems.
To play some games (e.g. Jackpotjoy, Gameaccount) you may need to pay to play. This can cost from as little as 10p a game and there's often decent cash prizes to be won. Click here for more details about prize games.
Loquax also has information covering Bingo, Casino and Betting related sites.