There's no easy way to do this currently (with the beta), but once the game comes out, I suspect it'll be much more accessible. Figured I'd post this while I still remembered.
What you need:
A model and all associated textures.
Lots of patience
The problem, in the beta, is with the first item. Models in diablo 3 are in the main data mpq, and this is in a folder called "appearance". Each model is a .app file in the mpq, which must then be converted to an .obj file.
There have been .app converters for D3, but the headers were changed during the beta for all of the different .mpq files, so they don't work anymore. You'll have to have the .obj and all the textures in one location.
Once the game is out, this shouldn't be a big deal. If someone makes a D3 model viewer, you may have the option to export it as an .obj file.
So then you basically just open it up in pepakura and get it ready to print. Here's some examples from StarCraft 2:
Below link contains examples and also the .pdo files that are used by Pepakura (kind of like a .pdf):