How-to: Click on image for much larger pictures.
Begin by determining the largest area of the shelf that can be covered by one continuous piece. Cut paper large enough (allow for 6 inches overhang on all sides, just to be safe). Coat with glue.
Coat the area of the shelf you will cover first with glue.
Lay the paper on the on the shelf. Start pressing down and smoothing out wrinkles/air/glue lumps from the middle out to the edges.
Continue with the same piece of paper and cover the top and under-side of the "sticking out part". Remember to continue to coat both the object and the paper with glue.
Once the paper is smoothed and well adhered, trim around the edge so there is approx. 1 inch overhang and make notches where the object curves. Glue down. Continue until all the edges are glued down to the back side and smooth the edges and front.
To cover the outer edge of the shelf part, cut the excess very close (you are aiming for the same width of excess as the edge of the shelf.
Glue and smooth down the excess from the paper covering the top of the shelf. Then glue and smooth upwards the excess from the paper covering the bottom of the shelf. Or vice verse.
The only part remaining uncovered is the shelf support piece. Cut two rectangles a little larger that necessary. Glue to both sides of support. Trim and glue the front edge of the support in the same way as the front edge of the shelf.
I chose not to cover the back of the shelf, but that could easily be done by tracing around the whole thing and cutting a piece slightly small than the back and gluing it down to cover the messiness.