In the contest design the rudder is of 3/4" pine, but I would recommend plywood if you can do it. I've used 1/2" ply, with the edges just rounded, and I've laminated two 1/2" ply pieces into 1"stock and shaped it into more of a foil cross section. (see leeboard) 3/4" would work fine too, and I know Jim Michalak sometimes laminates 3 pieces of 1/4" for his. Many woods will work, but ply is much less prone to split than solid stock.

I recommend you draw this full size on card board for a template. That way you can check it against the transom and with your hardware.

This is a kick up rudder that will pivot up out of harms way when you hit something. There is a disk of plastic sandwiched between the blade and the head that allows for generous tightening of the 3/8" SS pivot bolt and still have a  nice amount of friction. Keep you're mounting hardware in mind while you make this. Make sure the harware doesn't interfere with the pivoting blade. Sometimes it has to be countersunk. 

   The tiller is made from  3/4" x 3.5"stock 38" long. I drilled a  hole in it the thickness of the rudder head stock, then sawed to the hole to form the slot for the rudder head. If you round the head with a quarter round radius router bit, it can fit the slot perfectly. Very satisfying. Could be left square though. A stainless steel bolt runs crosswise in front of the head slot to prevent splitting. The hole in the handle end is for attaching a tiller extension if needed.

Option: You can see in the sepia photo above that I run my main sheet through a hole in the tiller that has been routed into a kind of smooth fair lead. It is above the rudder head in such a way that downward pressure on the tiller pinches the main sheet, lifting allows it to run free. This allows both steering and sail control in one hand, which I often find handy in small boat sailing.