I'm wondering how people build such well-balanced motors with perfectly round discs of plexiglass and pefectly centered holes in the middle of the plexiglass discs. 

Doug Konzen does this very well, for example.

Can someone here give some instructions for doing the above task?

Thanks
George

What you need is a router table, guard-free/guide-free ...   This need to be a large table with a means to drill and fix a peg at a known distance from the cutting edge of the router.

Make a center hole, use a peg the same size, fit snug, or something larger with an appropriate roller bearing for easy rotation, ..this is the axis hole.

Using a plunging/edging bit... you can rotate the piece around the axis peg while cutting.  Some router tables let you adjust the front/back position, this will let you fine tune a diameter.

Ideally you will need a high speed, sharp bit, it's always wise to get a new one and use it for finishing edges.

This is how they cut templates - , since it's got an axle hole in it, then it's a final piece too.

If I had a router, I would probably demonstrate this, but I'm lacking any tools right now.

Great, thanks.  That's perfect.

http://www.eplastics.com/Plastic/Plexiglass_Acrylic_Sheet

They claim to be cheaper than lowes (hardware store). It also seems that the stuff at lowes is hard to cut.

These guys will cut it for you too!

Another followup question here.

I would like to emulate Doug Konzen's pulse motor setup. Since he has done a lot of this, I wonder if he or anyone here is able to provide some nuts-and-bolts descriptions of his work: like the thickness of the plexiglass, the bearings he uses, etc etc... 

A list of suppliers would be awesome, too!

Thanks,
George