2x4 (buy whichever length you want, it depends on how many blocks you want, we just used scrap 2x4s we had around)
Something to cut your blocks with, a table saw or hand saw for rectangles and triangles
A hole saw and drill press for the arches and wheels (if you want them)
Sandpaper (various grits)
Sanding block (isn't necessary, but oh so nice)
Walnut Oil (found in the grocery store next to the olive oil)
Latex or rubber gloves
Step 1: Cut out a bunch of blocks in whatever various shapes you want. Brian did this part for me. He didn't worry about everything being exactly the same size, he just sort of went for it. Some of the blocks have holes where there used to be screws from previous things we built, but Ada doesn't seem to mind one bit.
It's not strictly necessary to finish the blocks, but wood has a tendency to "raise the grain" when it gets wet. So the first time your baby slobbers on them, they'll feel super rough like you never sanded them at all. A coat or two of a drying, food safe oil like walnut oil or mineral oil will help protect them from your little one's drool. Plus it's pretty.
Oh, and don't try using vegetable oil or olive oil or the like. They aren't "drying oils", and will get rancid over time. Which is unfortunate, because food safe wood finish is kind of expensive.
Safety Note! When you are disposing of a rag soaked in oil, beware of spontaneous combustion. As the oil dries, it heats up, and a rag which is bunched up in a bucket can and will catch fire. To dispose of it, lay your rag out flat somewhere far away from combustibles, and let it dry until it is hard and crunchy. Then it's safe to throw it out. I don't know how much this applies to walnut oil, but for many oils like boiled linseed oil, it is a very real (but easily avoided) danger.
You can see the difference in the finished and non-finished blocks here. The finished one is on the left and the non-finished one is on the right.
You're all done!
Enjoy little one!