The hard work is done now, and you're ready to glue the shelf together using wood glue and some clamps. That's just a matter of gluing the middle and face layers to the base, making sure that the the pieces are flush at one end and along the edges.
Make sure, as you do this, to keep glue away from the dadoes that the shelf supports will slip into. If those fill with squeezed-out glue, inserting the supports will be a challenge.
After that, add the blocks that form the notches near the other end.
Once the glue dries, slip the shelf supports into the dadoes to check the fit. Because the supports have plates at the back, you'll need to recess them if you want the shelf to sit flush against the wall, as shown in the drawing.
You can make those recesses by cutting around the plates with a utility knife, and then cutting out the recesses with a chisel. They don't have to be pretty.