I just built a shelf for a bedroom based on instructions found at Happy at Home. Problem is: the blog doesn't explain how to hang it!
Can someone help me figure out a clean way to hang this shelf that doesn't involve screws on the exterior of the shelf?
You could use a keyhole router bit to cut keyhole slots in the back to hang it.
Another option would be to use a french cleat. Either buy a metal one that could attach to the back of the shelf or integrate one into the wood back. Here is a discussion of french cleat techniques.
I installed big, heavy floating shelves in my house. The shelves are simple 2x10's purchased from a hardware store. They are pretty heavy and I knew there would be a lot of torque on any fastener I used. To hang them, I used 5/16ths threaded rods purchased from Home Depot. I cut them to about 7-8 inches long. Using a 1/4in drill bit, I drilled 4 holes into studs about 2 inches deep. I wanted the holes a bit smaller so that I could screw the threaded rods into the studs tightly. I then put two nuts on and tightened them against each other to allow me to have something to grab onto so that I could put the rods into the wall. Once they were in, I just drilled into the back of the shelves with a 5/16ths bit, making them as deep as the length left hanging out of the wall (about 5 inches or so). Using a rubber mallet, I placed the shelves onto the rods and hammered it into place. I basically just made this method up after having a brain storming session with a guy from HD. I've been very happy so far.
If the shelf is thick and deep enough, you could use a "concealed floating support bracket." I purchased a few at eBay. My picture of it below.
This particular concealed floating support bracket requires a 12mm diameter hole drilled into the shelf, about 100mm deep, to accept the long supporting pin. You'd also need to cut out some of the back of the shelf to embed the mounting plate within it. The inclination angle of the pin can be adjusted a little by turning the pin (using a spanner on the small flat part).
As a variation of this answer you can use any of these cabinet shelf hangers, called keyhole fittings, (which can be found in your local hardware store):
They are attached to the back of the shelf somewhere where the material is thick and strong enough. You have to make a cavity under the lamp-shaped hole so there's room for the screw head - the cavity can be drilled, routed or cut with a chisel, whatever is most convenient for you.
This is very reliable, and all screws will be hidden behind the shelf.
I recently had to do something very similar (using a door as a headboard, mounted to the wall). I ended up using these nifty little flush hooks.
They will leave your shelf 2-3 mm away from the wall, but if you have a router, you can rout a recess to mount the hooks in the back of yourself, which will make it completely flush.
They take pretty small screws, but appear to be able to take a lot of weight. There's not a lot of movement in how they slot together, so I would only use two, to avoid alignment problems.
When I used them, I mounted the hooks onto my headboard, then put double-sided tape onto the other hook plate. I then used a tiny bit of blu-tac to hold the other hook plate (the one with the double-sided tape on it) in place. I could then just line it all up, push it onto the wall (so the tape grabbed) then slide the headboard up. You're then left with the other plates stuck to the wall in exactly the right place. You can then mark the drill holes you'll need to make easily and exactly. This is harder to explain than it is to actually do!
I know you didn't ask for screws, but they do tend to be the most practical solution. A few screw options:
Screw into the top of the back just under the shelf, then tack up a bit of molding there to cover the screws.
Make the screws a decorative element. I've used 'countersink washers' for this before: 
For future use, attach the back to the wall first with screws where the shelf brackets will go. Then use a brad nailer to cover the screws with the shelf brackets (obviously not for shelves holding very heavy loads).
Look at French cleats. There are wood and steel options. Make sure you anchor them adequately in the wall as well as in the shelf back.if your shelf is hardwood, you can make the top wedge part of the shelf itself. http://www.newwoodworker.com/frenchcleat.html
Issues / concerns regarding some of these solutions:
(1) Weight - Amount of weight each option can support varies greatly. If mounting a shelf that could have up 75 lbs in total weight, need to know how many brackets to support that weight safely.
(2) Size of brackets - some of the large solutions like French cleats, etc, seem to be 3 inches in width (top to bottom), thus if the part you are connecting it to is only 2 inches wide, not really an option because part of the bracket would be visible.
(3) Mounting screws - "flush hooks" are nice, but the brackets (both sides) seem designed to be mounted to wood and come only with short wood screws that flush with the beveled holes. However, wood screws would not work well for mounting to dry wall. Thus you need to determine what kind of drywall anchor mount you need to support the weight and hope the screws that come with it, work with the flush hook brackets. The heavier duty the anchor mount, the bulkier the screw head that often will not work with the flush mounts.
