These shelves were purpose built to hold these cardboard box units, originally designed to hold trading cards. We call them 'faux' apothecary cabinets. My wife uses hers to hold craft supplies, my son to hold small Lego parts.
The red knobs are actually recycled lids from drink containers, bolted through the front of each drawer. This was my wife's idea and they work perfectly.
I used whatever scraps of plywood I could find that were big enough, and some that weren't. It turns out that 4' is the perfect height to make the 4 compartment unit, but that was the longest piece that I had. To make one that was 6 high I had to join the sides to shorter pieces with some smaller scraps.
This created a space in between the second and third shelf that I decided to fill with a drawer. Every bit of storage helps in our house. The drawer is another pretty crude concoction, made from 4 pieces of pine screwed together and then glued and nailed to a plywood bottom. That assembly was then screwed to the drawer face from the inside.
Right now it's kind of a 'secret' drawer, but I think it would look just fine with a couple of those fancy red pulls on it too.
As per instructions I attached casters to the bottoms so the units could be rolled to wherever they are needed.
Although they are not very pretty, they are at least solid enough to do the job. The sides are 5/8" plywood and the shelves are 3/4" thick and are glued and brad nailed into dadoes in the sides. The backs are 3/16' plywood set into rabbets and again glued and brad nailed. The face frame was sliced from an old 2 x 4 and attached, of course, by glue and brad nails. I must have watched too much New Yankee Workshop.
When my wife requested/demanded that I build these, she said "They don't have to be pretty, they just have to work." I like to think I delivered on both counts.