I found an excellent web site at http://www.projectdalek.co.uk/ that provides plans for building various models of Dalek. I've decided to build a classic "Genesis Dalek" from the 70's. This is the Dalek that I used to watch from behind the sofa as a child.
I decided to start off with building the Dalek's "skirt". This is basically the bottom half of the Dalek and is usually constructed out of wood. I read a lot of warnings about the health risks associated with MDF dust and decided to use the sort of plywood that is used for building model planes. This worked out pretty well but it was very expensive. I spent around $100 on the plywood and if I had gone with MDF it would have been more like $10 so I can see now why most people use MDF.
Once I had measured out the shapes I needed to cut from the plywood I used a Stanley knife to score the outline before using a jigsaw to cut the shapes out. If you don't score the lines first then the jigsaw rips chunks out of the plywood on the "up" cut. I later realized I could have just cut the shapes out directly with the Stanley knife for a much cleaner finish.
I used a 1 1/2" (38.1 mm) hole saw (a handy gadget that is a drill bit with a circle around it) to cut the holes for the hemispheres. I am going to be using 40 mm diameter ping pong balls for the hemispheres.
The plywood used for the panels is only 1/16" thick so I used glued wooden dowels along the join between each panel to give the skirt some extra strength.
Here's a photo of this stage of construction where I have a couple of panels glued on and the rest held in place with scotch tape.