If this sink was properly installed, it has two shut off valves that small hoses are attached to. These hoses lead to the underside of the "nobby" things on top of the sink. These valves apparently are turned off since no water come out when you turn the knobs. Disconnect the hoses from these valves. The large pipe coming out of the bottom of the sink is the drain. It should go into a P trap then into the wall. This should not be difficult to remove, but the pipe in the wall needs to be plugged to prevent sewer gas from entering the room. It probably already is since the water in the unused P trap has long ago evaporated. The actual removal of the sink from the wall will depend on figuring out exactly how it is supported and doing whatever is necessary. What you are going to be left with is an ugly wall with shut off valves and a drain with a rag stuffed in it. You might be better off to live with the sink unless you want to really get into the job of complete water line and drain line removal which will entail wall opening, a plumber, and carpenter. I say you will need the latter two people because by the nature of you question, you don't have even the basic knowledge of how to do repairs.