The first thing you are getting in to want to do is change to a sensitivity that you feel most comfortable with but, also helps you play the best. Most of the best Black Ops 3 players play on 4 to 7.
The second thing you are going to need to do is disable your controller vibrations. This will help you keep a steady aim throughout your gun fights and stay locked onto your target.
Something that most players do not do that will help you a lot is doing a quick warm up game. Just go right in to a custom game and put on some bots, and take off aim assist just for the custom game.
Another to better aim is to slow down and take your time. Lots of players play out of control. It helps a ton if you just slow down, take your time, and pre aim corners.
Another very helpful tip while to stay on target while firing your gun is that when your are shooting the gun take the left joystick and move it down and to the right. This will help controll recoil.
The last tip is very simple but is also very effective. Just put grip on all your guns if your struggling to control your aim and recoil while in a gunfight.