Here's a look at what I drew in Sketchup to help me plan out this project. The base would be a think piece of plywood. On top of that (well, on the bottom once it is hanging) would be a series of T-shaped and L-shaped tracks. The stemware would slide between two of those tracks, and hang upside down.

On the left side they would put some fairly large glasses, which need more space. Well to be clear, the tops of the glasses are wide, the bases are not. Therefore these will be supported with L-shaped tracks. Over on the right side would be where the smaller glasses go. Those can be packed tighter together so we'll build T-shaped tracks for that side.

Now, we could make T-shaped tracks on the left also, but they'd have to be quite wide. I decided to go with L-shaped tracks just to minimize the amount of wood being used.

Somewhere around this time my friend showed up to help build this project. Between showing him how to build this design, and doing the build and just general chatting... well that's a big excuse to explain that I managed to not get any photos of putting the tracks on the base.

There really was not that much too this process. We double checked the dimensions from the plan against the actual stemware. Then we marked front and back on the plywood where the tracks should be placed. Finally, we applied glue to the tracks and nailed them into place. For extra insurance we also drilled pilot holes and inserted screws from above. These would be hidden against the ceiling, so there was no aesthetic issues to worry about. I confess I've forgotten.

After that step, we took the unit over to the tablesaw and ran it through to clean up the edges and bring it down to final width.

That was the end of construction. My friend took the unit home and painted it. Painting was actually quite tedious, as there were many nooks and crannies on this project. A little while later I stopped by his place and took some photos of the final project, showing below.

Cheers!