How does satellites avoid collision?

The vast majority of satellites are in geo-stationary orbits. This means, they travel around the Earth at the same speed that the Earth rotates - making them appear in the same place. One example is the GPS satellite network. Other satellites that actually orbit around the Earth, are at a different altitude - so they would (thoretically) never collide with a stationary one. Those that are orbiting, are placed in such a way, that they also avoid each other.