There's only one game mode. The map starts with two special crates on it. If those are destroyed, two more crates are generated further up the line. If those crates are blown up, another two are generated further up.
You're either the attackers of the defenders. Attackers are in charge of pushing the line up and destroying all the crates. You can either shoot them with explosives(grenades, grenade launcher, C4?) or plant a charge on them, which is more efficient. You have only a limited number of spawns available, there will be a bar on your HUD to indicate how many you have left. Defenders have to defend those crates and hold the line. You have unlimited spawns. If a charge is placed on a crate you can defuse it.
Alternatively:
http://www.xbox.com/en-US/games/b/badcompany/20080627-multiplayer.htm