Start with the uprights
The backbone of this project is the uprights. They're the pieces from which all the other components are hung, so preparing them accurately is crucial. Start by cutting the four uprights to length, refining them with 1"-wide chamfers on the ends. Next, mark the position of the five notches that will accept the shelf supports, the angled brackets and soap shelf.
There is a trick to improve the speed and accuracy of the crucial notching operation; clamp the four uprights together, then use a carpenter's square to mark notches across all the pieces at the same time for accuracy. I cut the notches on my sliding compound mitre saw all at the same time as well. To do this properly, you'll need to extend the surface of the fence toward you with a scrap piece of 2x2. This is necessary to make flat-bottomed notches across all the uprights. Without it, the arc of the blade will leave a little ramp on the bottom of all the grooves closest to the fence.
Set the depth of cut on your saw to 1/2", then take multiple passes to clear out the waste. I like to cut the dado a hair shy of my layout lines and do a test fit with an accurately sized scrap of wood. This process results in a snug-fitting joint every time. Clean up the bottom of the notches with a razor-sharp chisel if necessary. Saw all of the 90° grooves first, then adjust the bevel angle of your saw and reset the depth of the cut to 1/2" to mill the 45° dados.
Once the uprights are complete, cut the shelf supports to length and cut 45º chamfers on the outward-facing ends. Cut the angled brackets to length next, adding 45º angles on their ends as well.
Before cutting notches on the underside of the shelf supports, dry-fit the shelf supports into the uprights and use the angled brackets to mark the position and depth. Before assembly, smooth all parts using 150-grit sandpaper.
Assemble the brackets
Attach the shelf supports and angled brackets to the uprights with an outdoor-rated Type II PVA glue and coated exterior grade #8 x 21/2" screws. Drill a countersunk pilot hole at each connection before installing the screws.
The next step is to attach shelf slats to the shelf supports with more glue and screws. I drilled all the countersunk holes (there are 40 of them) on a drillpress fitted with stop blocks to position them accurately. Once you're done drilling, position the brackets on their backs on a flat work surface.

4 Comments
This is a neat project. I made something similar but I put a potting spot in mine using an old plastic pail 25gal that I got free from a resturant.I cut a circle a piece of plywood and attached old plastic picnic table legs to the four corners stood it up and sank the plastic pail into the opening . I put pegboard on the back to hold all my tools.The plywood top is large enough for the pail and a work space and my sink. This was a very inexpensive project and something that I use a lot. I love it.
Can't make out what it is from the photo. Can't you do an "enlarge photo" of the accompanying photo? You have a really good magazine with very creative and unique plans. However, it would be very convenient if you would post the plans, with the accompanying article summarized, into one downloadable PDF. It's really tedious to have to print each page, pdf, and image individually. At the very least, could you make it so that the entire article prints -- without all the extraneous ads and web stuff -- when you click the "print" link, instead of each page???
This sounds like a great project, however I cannot enlarge the picture enough to get a good look.
that i agree 110% Very good sugestion.