All you really need is the right hinge, it's called a cafe hinge and you should be able to get one at any good hardware or home improvement store. You can see a diagram of one here:

http://www.swisco.com/catalog/drawer_cabinet.html

There is a bracket that goes on the top and bottom of the door at the edge which has a pin. Then there are brackets that mount to the frame with corresponding holes. A little plastic device at the bottom swings the door back into the closed position.

Dan

I have used both the "pin in the bottom" and double swing hinges - I can strongly recommend the double swing hinges for a smaller than usual door. The pin type depends on the weight of the door to make it close and if the door is too light it does not work.

The directions for the double swing hinges call for two hinges at the top and one hinge at the bottom. One at the top and one at the bottom is usually enough unless the door is heavy. I have also used the pin in the bottom (without the plastic insert with a single double swing hinge at the top.

We have a place around here that sells used building materials (and other things) for about 5 cents on the dollar. If you can find one near you, look at sliding doors - they come in all widths and you can probably find what you want. Watch regular doors - Marty is right - you can not cut down a hollow core door much at all.

The problem of the flat thickness is usually made up for by building either a special "Door Flat" with stouter lumber or just building a door frame/jam from 2 x 4 s and bracing the whole flat well to reduce waving and wiggeling as the door swings.
Marty W