While playing the game, you'll notice that other players are running around like chickens with their heads cut off, this is to pick up all the loot that was dropped by the enemies. You'll want to do the same, because you can pick up Mods off the ground just like they can.
After having enough mods, you'll goto My Arsenal in the game menu and you'll just upgrade, now if you're not familiar like everyone is at first, just use the R3 option to activate the menu to choose the Auto Upgrade option and the game will put as many mods on your equipment as it can.
The higher lever your weapon is the more mods and higher lever mods you can add to your weapons.