I should have used my old standby for wall mounting and use a piece of baseboard molding screwed into the vesa mounts on the monitor and screwed into ...
I needed a smallish desk for a space in my bedroom to last the 8 months or so until I move. I could have done this better, and made it more long lasting, if I'd used 1 1/8" plywood instead of 1/2" MDF, but it's good enough.
It was raining out, and my garage is so messy that I dare not photograph it, so I didn't build this out of a single sheet of plywood and a 2x4, but I could have. Instead I used a 2x3 that I had in the garage and 4 precut sheets or 2'x4' MDF at 1/2" thick. I needed a desk for the bedroom, because I was tired of not having one. I also wanted it to be something that I wouldn't mind throwing away in 8 months when I move 2500 miles or so, since it's crazy expensive to transport heavy/large things that far.
Step 2: Sorting out the legs
I measured for a desk surface 31" from the ground (most people will want 30", but I like being different.
Step 3: Putting it all together
Then, with my wife's help, I glued and screwed the "back" into the "top" and then the "legs" to the back/top assembly. Then I took the 2x3 and screwed it in at the back across the bottom, to keep it together while it's moved, and one across the middle under the desktop, to keep it from flexing. These might not be necessary if you used better joinery and thicker stock. If I were doing this to keep, I'd have used 1 1/8" birch plywood and only needed the one on the bottom.