Each satellite has an allocated location or orbit and its managers use on-board thrusters to keep it where it should be. When the propellant runs low, they use the last to de-orbit it in a controlled manner (barring problems).

Collisions are rare because when a satellite is launched, it is placed into an orbit designed to avoid other satellites. But orbits can change over time. And the chances of a crash increase as more and more satellites are launched into space.

In February 2009, two communications satellites - one American and one Russian - collided in space. This, however, is believed to be the first time two man-made satellites have collided accidentally.

You can have a pretty good Idea with this paper.

Chapter Development of a Debris Index

As George Dishman was saying S/C that are equipped with propulsion they can operate some collision avoidance maneuvers.

however not all the S/C have these subsystems. Therefore they need to use other kind of collision avoidance maneuvers that use orbital disturbances (gravity or magnetic field or drag) to actually move the S/C.

For instance: if the S/C has big solar panels or flaps they can be used as dragging surface. this will slightly change the orbit of the satellite. However, all is depending on the time frame and the effects of the disturbances.