Support can roughly be divided into artillery and support vehicles.
Using Artillery
You have two kinds of artillery here, medium and heavy. Artillery is very expensive, but can rain destruction down on distant parts of the battlefield. Do this by firing on the ground. If you hold the F key down, you can get a targeting reticule on the ground. Every artillery unit will have a dead zone around their immediate area in which they can't fire, designated by the green circle. Everything between that circle and the more distant red circle, however, is free game, so click on the ground to fire away!
Unfortunately for you, artillery is both slow to move and lightly armored; if enemy choppers or tanks get within range of your arty, it'll be toast before you know it. You also have to deal with enemy tactical aid that'll be coming your way, and come it will! If your enemy can see your units directly, then there isn't much you can do about this, but even if you think you're well away from enemy forces, get in the habit of moving them after each barrage of rockets. You don't need to move too far, but you do want to
Although artillery is the preferred choice of the loner, since you don't have to really do anything but guard your own vehicles, you should still be on the listen for teammates that are calling for artillery. Even if you're not grabbing control points yourself, you can still help your team out by supporting them and destroying enemies that stand in their way.
Defeating Artillery
Artillery, as mentioned, is very weak. If you can roll a heavy or medium tank or two into the vicinity of artillery, you can toast them pretty quickly. However, a good commander will keep his artillery far, far away from the combat, in a corner of the map where no one will think to look for him. Thus, finding him is often going to be the most pressing concern of yours.
Luckily, it's pretty difficult for artillery to be stealthy.
Both medium and heavy artillery will leave behind trails in the air
when they fire, with the trails of the heavy artillery being
particularly easy to spot, especially on the NATO and US sides. Medium
artillery trails are more difficult to spot. Still, if you find
yourself getting hit by artillery, start looking for trails and try to
follow them back to their source. If you can do so, you'll often see a
bunch of trails starting at a point near the ground, then disappearing.
This is the location of the enemy artillery. The best part here is that
you don't need to be able to actually see the artillery to trace the
smoke trails back to the source; the smoke trails appear as soon as the
artillery fires, and is visible to you no matter where you are on the
map.
Using Support
In addition to the artillery, you have three other support units that can be used to help your team achieve victory.
Heavy Anti-Air
The heavy anti-air unit is capable of quickly taking down any choppers that come anywhere within a fairly long range around it. It fires heavy-duty missiles that will track down enemy aerial units and rapidly damage them. These can be avoided if the chopper drops flares, but this will be difficult for most players to do before they get hit a couple of times.
Medium Anti-Air
Medium anti-air units can blast helicopters that come within their immediate area. They use machineguns for this purpose, and as such deal damage more gradually, allowing enemy choppers to escape without much damage if they notice that they're getting fired on. However, these rounds are fairly difficult to see in the heat of a pitched battle, at least compared to the rockets of the heavy anti-air, so you can sometimes take out choppers without them even noticing that they're getting hit.
Medium anti-air units are also unique in that they can turn their guns on ground units to fire on them as well, assuming you use their offensive ability. This is mostly useful against enemy infantry, but even then you shouldn't expect to kill too many units with it.
Repair Tanks
You're going to be using repair tanks a lot during the single-player campaign of the game, so if you play through that, you should have a good idea of how useful they are. However, since they're grouped with support instead of armor in the multiplayer portion of the game, they probably won't be used quite as often. They can still come in handy if you play solely as a support player, in that you can repair any damage your artillery and anti-air units take, but in most cases, if you take damage at all, it'll be of the catastrophic and instantaneous tactical aid sort, so you'll just wind up losing a repair tank in addition to your other units.
Using Support as Support
If you want to actually play as a helper, you can try to team up as a support class with someone who's playing armor and move together. If you share the same drop zone and can keep your movements coordinated, then a few anti-air units and a couple of repair tanks will let your armored friend worried about enemy ground forces while you deal with the sky and keep him repaired. Unfortunately, most smart enemy players will target your repair tanks before firing on the tanks that you're repairing, so you can expect to have to redeploy them pretty often.
Defeating Support
Repair tanks aren't difficult to take out if you can get close to them. They're lightly armored, and although they have a self-repair power, it takes a while to work, letting you kill them pretty easily. Anti-air units are another matter: they'll fall easily to tank fire or anti-tank soldiers, but will keep choppers at bay. That said, if you can mass your choppers up for an attack, a couple of hellfire missiles will do a number on your foes without too much of a problem, and you won't even take all that much damage if you're facing off against a medium anti-air unit. If there are two or more heavy anti-air units in an area, though, you'll need to find some other way to take them out.