Lighter then air vehicles like balloons, blimps or zeppelins. They use one or more gasbags to provide buoyancy. Common gas used is hot air, hydrogen or helium. For a balloon lift can be simulated with a single force that pull that balloon up and counteract gravity. The balloon simply drift with the wind to move. An airship can have propellers placed around it to move the ship and then one can apply forces at them.
AirShips.Net - 2006
There are four main forces on a airplane. They are gravity, lift, thrust and drag.
Gravity: Tries to pull the plane towards earth like always.
Lift: This is generated by the airflow across the wings and the rest of the plane. The contribution of each part of the plan is calculated and then summed up. If lift is larger then gravity the plane goes up.
Thrust: From the engines and push the plane forward.
Drag: The friction as the plane moves in the air. Opposite to thrust.
Gravity: Tries to pull the helicopter down.
Lift: A helicopter use the same basic principle as airplanes to fly. The rotor of the helicopter generates lift by spinning fast enough the same way the wings of a plane generate lift by moving the whole plane fast enough. By changing the speed of the rotor one can generate more or less lift and that way use it to change height.
Tail Rotor: The trail rotor is used to counteract the main rotor. The rotation of the creates a torque that try to rotate the body of the helicopter. The tail rotors speed can be changed to cause the helicopter to spin around on it axis (yaw) and face another direction.
Unity3d Helicopter Tutorial - 2010
Implementing realistic helicopter physics in 3d game environments - 2002