Have you played I of the Dragon? It's an action game where you are a dragon, fairly similar to Gauntlet. Movement in that was quite simple. Two keys adjusted your altitude, and you clicked on the ground to move above that point. A column of light shone from the ground where you're moving to, and a ball glowed in the column at your selected altitude. The dragon made his own choices as how to fly and turn there. Clicking on enemies would attack them with the selected weapon. If you selected a melee weapon (ie. pick them up in your claws and eat them) he'd swoop down and catch them mid-flight and then return to the safety of the skies. Regardless of whether you levitate or fly as a bird, this method can work.
As for combat, it very much depends on if it includes levitation-style, bird-style or both. Birds swooping opponents, raking them with swords and axes would be very impressive. Two birds fighting each other could be tricky. I've never seen AI handle this well. They usually end up circling each other getting nowhere.
For a levitator, combat can be roughly the same as ground combat. The main difference is the massive defensive bonus the levitator has. Anything fired at them would be over a longer distance and have to contend with wind, etc. A levitator throwing anything explosive at the grounded will have the benefit that even if they miss, the object will still explode upon hitting the ground. The grounded don't have that advantage throwing things into the air.
Another good point is gravity. The grounded strugle to shoot high enough to hit fliers. Of course, gravity works both ways. Should the flier take sufficient damage to knock them back in combat, the ground they fall on is a lot further away now.
There could be a whole sub-set of airborne combat skills like Swoop, Ride Wind, and any number of wind related spells and abilities.