Airbenders have the ability to control and manipulate the air currents around them either defensively or offensively. Defensively they can rapidly swirl the air around them to block or deflect an opponent's attack. Or, like Aang, use a staff to swirl the currents into a shield. Offensively they can create a jet stream of air which can be blasted at an opponent's chest to knock him down or pushed with lightening speed along the ground to knock him off his feet. They can also create wind funnels to channel objects through or lift an opponent up and spin him around until he's too dizzy to fight. By running rapidly around in a circle, they can also create a tornado. In addition to their ability to control the air, Airbenders are also very agile on their feet and very fast making them almost impossible to catch. They can literally run circles around their oppenent confusing and exhausting them while they lead a counter attack. Airbenders also use the air currents to help them spring upward to great heights or to jump over and around an opponent, or to run briefly along walls and across ceilings. They can also break a fall from a great height by creating a cushion of air as they land. Lastly, with specially designed gliders they can fly.
The Bagua (Circle Walking) style of Martial Arts
The movements of Airbending are based on the Bagua style of Chinese martial arts often called "Circle Walking" which incorporates unique circular series of fancy footwork, coiling and uncoiling of the body and rapid changes in direction, along with defensive and offensive hand movements. Circle Walking has three intentions: to confuse an opponent, to exhaust them, and to draw energy evenly from all directions. It is especially good for combat with multiple opponents and close contact fighting since the oppenent can never seem to turn fast enough to keep up with them. The hand movements are circular with palms facing outward towards the opponent. The torso is turned towards the center while feet walk the edge of the circle in an eight step pattern that circles the opponent. (source for info on the Bagua form of marial arts: bagua.hollosite.com)
(thank you BlueSigma for the link)