Judging from the pictures, it appears that he used 3/4" particle board. And judging from three of the pics where there's a jigsaw in the background, I'd guess that he used a jigsaw to cut it.

I agree with JAMF on the material selection. 1/2" MDF would be more than strong enough for a shifter mount. They should be able to cut it up into more manageable sizes for you at whatever home improvement store you get it from.

If you want to go the powertool route and not the hand tool route as JAMF suggested (and save yourself an aching back and arm but up the potential for lost fingers), grab yourself a cheap jigsaw. THIS is the saw that I picked up from Home Depot for $40. It's done stellar work on my cockpit project. Get the blades for the finer cutting, keep the speed medium to low and be patient when cutting.

Just remember to keep account of where your spare hand is AT ALL TIMES. You could easily forget that you're grabbing a board right near where the cut needs to be, and slice right through your fingers on the underside of the board. That nearly happened to my buddy who was helping me with my pit. I was so concentrated on getting the line laser-straight that I wasn't paying attention to where his hand was. He moved it just in time, right before I was about cut off one of his fingers!

That said, my jigsaw is my favorite tool now. My only other options when cutting before I got it were my circular saw and my reciprocating saw, or "Sawz-all". Neither of which will give you anywhere near the dexterity needed for projects like this.

If you're planning on doing more than one of these kinds of projects, I'd recommend learning to use Google SketchUp. It's a very simple to learn 3D modeling program, and I've used it to prototype everything in my pit build so far. I find it much easier to just start going at it in SketchUp. In 30 minutes I have a good idea of how everything's going to look and fit together, and with another hour of perfecting and refining you've got all the measurements you need to start drawing on your materials IRL. Hell, SketchUp has become so easy to use for me now, I started modeling my garage and everything in it just because I'm thinking of rearranging the place.

If you don't want to learn SketchUp, I'd recommend cardboard as a prototyping material. Glue a few sheets together to reach your desired thickness and go to town with it. Eventually, when I get far enough in my pit build, I'll be prototyping the pit's enclosure in cardboard.

For Cutting with the jigsaw, do you just lay the wood down on horses and let the part your cutting hang over?

That's how I do it, but I'm by no means anywhere near an expert.