Slingshotting of players is accomplished by crouching or proning on top of a friendly vehicle (typically a ground vehicle), and having the vehicle move backward. At some point, the player on top of the vehicle will inadvertently be launched opposite of the vehicle motion. It appears that the player is unable to use their parachute, and may suffer heavy Fall damage if he impacts against a vertical surface. The player also gains enough momentum to break through objects like wooden fences.
Certain ground vehicles such as the LAV-25 are susceptible to getting stuck on terrain. If the vehicle has been spinning its wheels/treads, and is shoved free by another vehicle, the freed vehicle instantly gains speed as if it were "stored". In many cases, the launched vehicle will move much faster than it normally should on its own power.
On another note, if the same vehicle (LAV-25) is moving at a fast speed towards water, the vehicle might launch high into the air, usually in the opposite direction.
A player can also be slingshot by proning in front of a friendly MBT's main cannon, which it then fires, launching players a considerable distance.
Like Car Launching, slingshotting can potentially be used to discreetly move players across the map.