This link will give you the basics and a decent equipment list:
http://badmanstropicalfish.com/paludarium/paludarium.html
Get some acrylic sheets, pvc, acrylic saw blades and hole saws, and a lot of sealant...and you're good to go.
I recently put together a little paludarium tank (not really a river tank), and I used some of Badman's (see link) ideas. Though I didn't agree with him on all the choices he made, he still had a very good equipment list and "how tos."
CoNMaN: I used this approach (including the slate) to build a waterfall and shallow elevated pool in my tank. It works well. I also made a little acrylic "box" to put the filter or filter media in, so no equipment is visible.
Note: Since these tanks usually don't have much water in them, you may want to consider using an overflow/sump. If you do, you won't have to bother with drilling the acrylic...just overflow from the tank in the deepest pool and pump back in from the sump at the most elevated pool. And it increases the water volume...
Good luck! Its quite the endeavor.
- mb