Here are some tips that might help you.
Learn to move and shoot. That is key.
Learn the placement of weapons and health around the map. Spend some time exploing the maps by your self.
If there are vehicules, play around with them. Learn to drive them well. See if you can drive vehicules into the buildings or anywhere on the map.
As lame as this may sound, play against bots before people. Bots are easier and predictable, this way you can learn when to shoot, what to look for. Also, bots generally wont beat you into the ground so it gives you time to look around and figure out good vantage points for sniping. When you do well against bots, up their difficulty. I got great at shooters by playing against bots all the way back in Timesplitters for the ps2.
If the game does not have bots the play with a friend. Split screen is best, but if not then online. take time to practice shooting while they are running sideways, while you are running, jumping, driving, etc.