You have to hold down the action key you use (usually X or the left thumbstick). You need to hold it down for around 5 seconds so you can use the item.
The weapons you start with are all you get, outside of a few weapons you get by completing the challenges.
Aaaaand there are OBJECTIVES in this game... That's how you beat each mission, not with kills.
Shoot me a friend request on XBL, my gt is L00fah (same as it is here, with zeroes). I'll help you out sometime.
Did you happen to read the manual oooor anything? It teaches you everything you need to know. I also recommend doing the Challenges as a newbie. They're extremely informative.