What sorta primary are you using? Make sure you have one with a decent impact rating, damage seems not to matter very much if at all. Use your grenades to do some damage before you actually see them coming around the corner, and if your running towards each other chewing up health just melee to finish. Grab heavies as much as you can and stay stocked on special ammo, even if your pretty full it stops the enemy from grabbing it.

Multiplayer takes some getting used to overall. What level are you? I recommend playing single player until you have some decent loot/armor/weapons. I've found specific guns (primary guns with a high rate of autofire and secondary guns such as shotgun or charged lazers) do the most damage. Gun stats do carry over, aim for the head, remember to melee, and play with teams before entering rumble. You'll get the hang of it eventually. If multiplayer isn't your bag though, PvE is pretty great when playing cooperatively. Loot loot loot. The better loot the better you'll do in PvP