Normally the participants would bring their own computers. For every person you would need at least 2 plug in spots for power, one for monitor and one for computer. Most LAN competitions impose rules on the size of monitor you can bring to save space, also most require that you use headphones instead of speakers. You will need some kind of network that everyone can access. Depending on what game you would likely need a computer to run a dedicated server for the game.
Popular LAN Party games are:
Counter Strike Source
Battlefield 2
Day of Defeat Source
Google brought up these sites they seem like they are probably of use:
http://onepc.net/index.php?view=docs&doc_id=75
http://www.lanparty.com/