A RepRap-style printer (technically, a fused-deposition-modeling printer) works by squeezing molten plastic out of a hot nozzle onto the workpiece, where the plastic cools, forming the next vertical layer. One FDM printer can create some of the parts for another FDM printer, or to replace its own parts when they get worn. This was the idea behind the RepRap project, that partially self-reproducing printers could be very cheap.
Stereolithograhic 3D printers operate on a different principle, using ultraviolet light to cure resin. The video above illustrates this process.

My printer is pretty crude and is due for a lot of improvements in the days ahead. I had ordered a stepper motor controller board that didn't work, so I needed to manually rotate the threaded rod that lowers the workpiece into the resin bath.
Hopefully this picture isn't too confusing. A lot of this is stuff from the hardware store: a bucket, a lot of plywood, nuts and bolts, a piece of aluminum screen, a threaded rod, two straight rods. That black shape at the top held in place with a bungee cord is a pretty standard conference-room projector. When the thing is printing, the projector aims down into the bucket, which holds a quantity of resin floating on a much larger quantity of salt water. The ultraviolet light from the pattern projected onto the resin cures it in a particular shape, forming one layer of the product, and then the threaded rot rotates, moving the product down by one layer-height.
Currently I'm using a layer-height of 1/40th of an inch, which turns out to be quite visible to the naked eye, so I want to go down to something more like 1/100th of an inch.
I plan to post plans and software on Github and Instructables to enable anybody to build one of these printers for just a few hundred dollars. Most of the cost ($350) is the projector. I'd like to do the RepRap thing of using lots of pieces made by an identical printer, which would involve some redesign.