Prepare the shelves and supports. Test the fits of each joint to make sure everything lines up and sits how it should. Finish the shelves in the manner of your choosing. I covered the top of each shelf with wood veneer.
If you used the cut-away glasses holder method I suggested during the layout, glue your pieces together. I cut holes for the dowel supports. When I glued the shelf to the glass holder I had the dowels in place to make sure everything was lined up just right.
When I placed all my shelves together with the sides in place the glasses didn't fit exactly how I hoped. Upon further inspection the was a little bit of variation in the sizes of the glasses and the laser cuts at a slight angle. A little bit of sanding and the glasses fit perfectly.