Here is a SketchUp model of some wainscot and vanity I designed and built for a half bath.
The room is about 4-1/2' wide and 5-1/2' deep. I built the wainscot sections in my shop from hard maple and maple plywood for the panels. The vanity was built in the same style. I finished everything with BIN pigmented shellac primer followed by BM's Advance paint. This was the first time I've used Advance and I really like it other than it takes a long time to get hard.
I installed the wainscot panels by screwing them to the studs only at the very top and bottom where the trim and baseboard would hide the screws, leaving just a few nail holes to fill on the cap molding and baseboard.
Good photographs were hard to get but these should give you an idea of how it turned out.
You may notice that I changed the design of the molding around the vanity. I decided that the original design would be a trip hazard with the vanity being so close to the toilet, so I got rid of the plinth blocks and wrapped the baseboard under the toe kick. It doesn't look quite as good, but it's safer.
Somehow I didn't build a panel for the short wall to the right of the door. The owner thought he told me he wanted one, but I don't recall it. I'll make him one sometime this Winter, but in the meantime I needed to cover a gap at the bottom of the wall where he had removed some old baseboard. I held a piece of the new baseboard up to the wall and it didn't cover his new tile. Hmmm. OK, how about this, for now?
Once he paints the wall it should look OK. The "shoe" molding is just a piece of the cap molding that I ripped off.
John