Cooperative play
From Halopedia, the Halo wiki
Co-op is a multiplayer gametype found in all Halo games except Halo PC. It allows two or more people to play the campaign together. If one character dies, he or she will respawn with the weapons they begin the level with. The player who dies has to wait until the player who is still alive is not engaged in combat and is at a safe location to be able to respawn. If both players are killed, both you restart at the last checkpoint. Additionally, in Halo 2, if you are playing on Legendary and either of you die, both of you have to start at the last checkpoint. Though in any of the other Halo games, nearly all players will do Legendary on co-op, because legendary was created to be hard
In Halo 3, when there are two players, one player will be Master Chief and the other will be the Arbiter. It is somewhat the same with three players, with the addition of N’tho ‘Sraom as another playable character. If a fourth player is available, the Elite Usze ‘Taham will be playable. It should be noted that the players can not choose who they play as and the game will randomly select who plays as who. Co-op can be played on split screen on Halo and Halo 2, but can be played either split screen or over x-box live in Halo 3.
Co-op Game-play
Co-op game play is very different from single player, there are several things that you can do (with the exception of Halo 2) in regards to gameplay, this part of the article is meant to tell you some strategies that you might find useful in your game. It is assumed that you are playing on Legendary difficulty.
Strategies
Coward Method
First and foremost, there is the "coward" method, basically player A stays back in a safe spot while player B charges forward and kills everything with impunity, this method is frowned upon greatly, and is used commonly, though it cannot be used in Halo 2 on Legendary. The best way to use this method is to play as the Arbiter in Halo 3, and to alternate players so that everyone gets a turn, or you can have one sniping, so the player is not necessarily safe, and is contributing.
Full Shotgun
Both players charge the enemy, though this method is harder, it will make a more enjoyable playing expierence, and will be a true test of skill to get through levels, though this is useless for single player expierence
Run and Gun
Attempting to get through the level as quickly as possible while also trying to get the most points possible. This method often involves vehicles and ignoring many enemies that you may otherwise be inclined to shoot. The reasons players do this is generally because they only want the legendary symbol for their Xbox Live Account, or they may wish to get the meta-game achievement by relying mainly on the time bonus for the level.