Ability to take out enemy AA guns is the most important skill for new players to master. In the early game AA guns are the dominant feature on the board. Learning the techniques presented herein should have you tearing through them in no time.
The cheapest method, ammunition-wise, is to let your ground forces deal with the gun. A tank or a squad of infantry can destroy it at close range. Unfortunately, there are many situations where this can not be applied. Hostile bunkers mow down infantry. AT guns shred tanks. And enemy copters swat both infantry and tanks. So other tactics are often needed...
The best players can drop a pile of bombs precisely on top of a gun from a relatively high distance, and usually only take one or two hits. However, this takes a lot of practice.
Try unloading rockets at about one screen of distance from the gun. Again, accuracy improves with practice.
Another way to do it safely: take your gunship very low, 1-2 pixels off the ground, and then fire two radar guided missiles. If there are no enemies between you and the gun, they'll home in and take it out. This tactic can work from over three screens away!
When ammo runs low you still have one good method of defeating the AA gun: ramming! Fly over the gun at about three helicopter heights, brake hard while unloading your bombs, and steer your copter into it. Sometimes this will be enough to take it out. Just try not to catch too much flak on the way in, or your copter will explode before closing the distance.