How can I set-up a common dish network to be used by all residents in an apartme

Short answer is to call the provider and see what they have to offer. You have both legal as well as technical issues here. Most these satellite companies have plans and packages to provide this and generally require that they install it.

Generally the solution is no different than sharing any internet connection and there are lots of post here and elsewhere on how to do that. The key difference with satellite is that it has a very low bandwidth cap and the more users the faster you hit this cap.