How to mate two flat pieces of wood at a point about which both can rotate?
I would not use a bolt for this, although you can. There are various ways to do this. The simplest just requires a rod and two push caps.

Drill a hole through the wood and sand it with a fine circular file to fit a rod. Cut the rod to size using (for example) a cutoff disk. Get two push caps and use them to secure the rod/axle. Push caps look like this and you can find them in any hardware store:



They are also called "roller caps". To make a smoother action you can insert a bushing in each piece of wood, but that is probably overkill.