Cloth simulation and soft body simulation are very similar in Blender, despite a few key differences. Both soft bodies and cloth work on open as well as closed meshes — that is, the mesh could be flat like a plane or more of a shell like a cube or sphere. However, soft bodies tend to work better on closed meshes, whereas cloth is better suited for open ones.
Also, the cloth simulator tends to work better with self collisions. Think about the fabric of a flowing dress. In the real world, if you bunch up part of a dress, it's technically colliding with itself. In computer simulations, you want to re-create that effect; otherwise, the fold of one part of the dress breaks through the fold of another part, giving you a completely unrealistic result. The cloth simulator handles these situations much better than the soft body simulator.
Revisiting the simple default cube, here's a quick walk-through on getting some cloth to drape across it:
It doesn't have to be too high; just a couple of units should be plenty.