The biggest protection satellites have against collisions is the fact that space is huge and the satellites are small. So the chance that two satellites are in the same location at the same time is extremely small. You can launch a satellite into a random orbit and have it orbit for fifty years and still not expect the satellite to crash into anything major.
But just in case they do usually pick orbits based on what they are doing, so most satellites that does similar things end up moving in the same direction and therefore do not hit each other. And there is databases of all the satellites and their orbits so you can check if the orbit you plan intercept any of them. Satellites do randomly shift their orbits so these databases are constantly updated using radar tracking stations. They use the old radar stations designed to detect incoming nuclear missiles but these have not gotten enough funding for the past thirty years so our coverage is getting worse. When a radar station detect that two satellites would get close to each other they will attempt to contact the owners of the satellites. A lot of satellites have thrusters and are able to move a bit to avoid a collision. So far there have only been a handful of satellite collisions.
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