This is a very easy wall shelf to make. It is constructed using rabbet, not rabbit, joints. Poplar isn't the best staining wood, but if you use pre-stain conditioner it can turn out alright.
I resawed some poplar into about 1/2 inch thick for the sides and the shelf.
I used my new planer to remove the saw marks.
I cut the sides the same length as their width.
And I cut the shelf to length.
I used a sanding drum and hand sanding to smooth the curve.
I used a straight bit in the router table to cut rabbets the thickness of the sides pieces. I made a rabbet on one long and both short sides.
Now I cut the back to size.
The top was too wide, so I trimmed it down.
I sanded the insides before gluing.
Using the drill press, I made 1/2 inch holes for the mounting screws.
Then I glued it all together.
After it dried, I sanded the outside, making the bottom of the back panel match contour of the sides.
The fit on this rabbet stunk, so I some thin scraps I had and made trim out of it
I fastened the shelf into the studs and used some pre-made buttons to cover the screws.
Free plans are available in PDF and SketchUp formats.