You need one of the following tools: an adze, an inshave, a pullshave, or a collection of hand carving gouges. Or all of the above. Try to find information about chair making, since chair seats are usually shaped in a concave fashion. The Windsor chair, in particular, uses many of these tools to shape the seat.
Edit: all of these tools are designed to be used in solid hardwood. Which means that plywood, particle board, and MDF are probably out. If you purchase new versions of the tools, I wouldn't expect them to be sharp enough to cut well. Be prepared to sharpen them before and during usage. If you don't know how to sharpen curved tools well, you'll probably become frustrated very quickly.