Most will already have all the tools needed to make a cup. If you want to go very simple you can make it with only a saw, a knife and a hand drill.
But the marking gauge and the power drill makes it easier.
The ax, the froe and spookshave are used to make the bottom.
If you don't have a suitable knife look at my instructable showing how to make the perfect carving knifehttp://www.instructables.com/id/How-to-design-and-make-a-perfect-carving-knife/