It's just like completing objectives in single player.
Set up some sort of entity with an objective number set in it's properties. (There are tutorials on objectives that you can find, most likely in the official community guide by Nickydude)
There are workarounds to getting dynamic entities in multiplayer mode. You can use this to your advantage for objective multiplayer games. Like, have an obstacle course type game, where each player starts at the beginning of a different obstacle course, complete with targets that they must shoot (These will be destroyable objective entities), and then reach the center of the arena and step on the glowing pad (Winzone with another objective). If they missed any targets along the way, then stepping on the pad will not make them win until they go back and shoot all of the targets that they missed.
Of course, that's just an example, you get the idea, right?
The one and only,
Whosoever says, "Don't sweat the small stuff," is obviously not a programmer.
