Two things to note before you embark, 1. This shelf is great for light and simple use -- to hold a picture frame, etc. Depending on how it is mounted will determine how much weight it can bare. 2. When I initially started I thought this would be a piece of cake, but it turned out to be a little bit more difficult as the project progressed. To Start I recommend buying wood 1" think or more, I was using 3/4" Laminated Pine for Shelving, additionally, you should experiment with different mounting options, the nut and bolt's that I use for this were found cam lock and screws in the special items drawers at home depot, but there are other options out there.
Step 1: Here's What You Need
When our initial piece of wood is cut into a right triangle that is 18" x 18" x 25" we will cut into that piece two inches from each side to give us stability when mounting. Each time we make a cut the table saw is going to each some of the wood and will throw our per-determined dimensions all out of whack. So if you want and 18" x 18" x 25" exact corner shelf, I recommend buying an even larger slab of wood.
You will also need are called Cam Locks and Screws (2nd Image)
And a 5/8" Forstner drill bit which will cut and leave a flat base. ($8) (3rd Image)
Step 2: Cut the Triangle
Step 3: Prep Sides
You should end up with pieces like the images below.
As I mentioned before, when the cut is made, part of the wood will be out of alignment, to fix this you can just cut the extra length off from each piece (the easy way), or do what I did and match the grain make both a flat cut and a 45% cut. (The hard way).
Step 4: Now the Hard Part.
Try a piece of wood to test your drilling skills on before going at the final work. If you drill the forstner bit too close to the edge then your screw / bolt will stick out too far. The circular lock has to sit in deeper than normal, so place the bolt down and draw where to cut.
Step 5: Almost There
Then use the same bit to create recessed holes in the side pieces. I put two holes in both side pieces so that I can make a strong connection into the wall.
Step 6: Rough Assembly
And hey, I flipped mine over and it's pretty good, but needs some pieces cut off from the ends. (Off to the bandsaw).
Once it's cut and cleaned up. Your pretty much done, just drill holes in your wall, insert, screws, and install.
I used a wood stain before mounting.
Hope you liked this breakdown and hope it helps your to avoid some of the mistakes I've made.