Rip all pieces to width now, then cut to length. It's especially important to cut the ends of the rails exactly square, since the tenon-cutting technique I recommend relies on this to give you square shoulders.
Mark locations for the front rails on the front legs, and cut mortises into the left and right inside faces. There are many ways to do this, and I usually opt for a plunge router technique. Clamp two legs into your bench vise, extending past the vise so the router fence is unimpeded. The leg closest to you becomes the guide for the fence while also creating a greater bearing surface for the router to slide on. The leg behind gets the mortise first. Fit your router with a 1/4" up-cutting spiral bit to remove the waste, then square the mortises with a chisel when you're done. Repeat the process to cut mortises in the neighbouring leg.
Like mortises, tenons can be cut in many ways. After marking tenon locations in pencil, I like to remove the bulk of the waste with a bandsaw, then finish up with a table-mounted router fitted with a straight bit. Orient the rails end down, with a square piece of plywood against the fence behind the rail, to boost safety and control.
The back rails and legs now need a 1/4" x 5/16"-deep grooves to receive stub tenons as well as the plywood panels. This can be done with a dado blade in the tablesaw or a router spinning a 1/4" straight bit. Centre the groove in the rails in the 3/4" stock. The grooves in the legs should stop three inches short of the bottom.
When you have the stiles and rails cut, assemble these parts without glue and measure for the size of veneered plywood panels you need to fit within them. Test-fit again with everything in place, then put these parts aside for now.
Next comes the drawer. Cut the required parts, including the solid pine drawer front. You can put a drawer together in countless ways; I chose something unusual. The drawer front joins to the sides with one large, half-blind dovetail at each corner. The drawer back fits into dado grooves set 1 5/16" from the back edge of the drawer. This keeps the drawer from tipping forward when fully open.
You can cut the big dovetails with a handsaw and chisel, or devise a simple router jig, as I did. This allows a dovetail bit to do the bulk of material removal, followed by some handwork with a chisel to square up the corners.

2 Comments
I did not see any plans.
I saw the plan is linked at the place "Download the plans for this project here!", it is very detailed. Thanks for sharing this project! Nice job.