These are far from the prettiest hanging shelves on instructables, but they may be the simplest.
Step 1: Materials
Step 2: Drill holes in the corners of your shelf
Drill a hole in each corner of your shelf. 1/2" from each side is fine, but it doesn't really matter.
More important is the size of the hole. You want it to be just big enough for your string.
Step 3: Cut string
You can use one long piece of string or two shorter pieces. I'm going to describe how to do it with one long piece because it's easier.
Measure your string using the board for your shelf. You want your string to be as long as one length plus four widths.
My shelf was 17" long and 9" wide, so I cut my string to be 17" + 4*9" = 53". This will likely be longer than necessary.
Step 4: Thread strings through shelf
My string likes to fray, so I put scotch tape on one end. Tie a knot in the other end of the string. Start with the figure 8 knot shown above. Test the knot by trying to pull it through one of the holes you drilled in the corner. If it won't go through, you're good. If it squeezes through then try a larger stopper such as the oysterman's.
Step 5: Threading string through shelf, part 1
Starting from the bottom side of the shelf, push the taped side of the string through one of the corner holes (1). If you care which side is the front, start from one of the front holes. Pull the string all the way through until the knot stops hits the bottom. Thread a washer onto the string, then run the string down the nearest corner hole (2). One side of your shelf is just about done.
Step 6: Threading string through shelf, part 2
Run the taped end of the string up the hole on the opposite side (3). Thread the second washer on the string then run the string down through the last hole (4).
Step 7: Tying the second knot
Estimate how low you'd like the shelf to hang and make both sides about equal length.
Flip the board over and tie a knot in the dangling piece of string. If you're not sure how low you'd like your shelf to hang, start with a slipknot. That way you can easily untie it to test different heights before tying your final figure 8 knot.
Step 8: Find yourself a stud, or use a wall anchor
My favorite stud finder is a rare earth magnet. I slide it over the wall until it sticks. It finds the screws that attach the drywall to the studs. For plaster walls, a magnet will not work, and an electronic studfinder may or may not work.
Step 9: Mount one side of your shelf
Hold the shelf up so the knots are in the front. Thread a screw through one of the washers and drive it into the wall. Almost all the way, but you don't want it pinching yet. I like to predrill with a 3/32" bit.
Step 10: Mount the other side of your shelf
Find another stud or get another anchor ready. If you have a level, you could use it to mark the height of the second screw. If not, you can eyeball it. Thread the screw through the washer and drive it into the wall. Again, don't pinch the string yet.
Step 11: Make your final adjustments
You want to adjust the shelf front to back as well as side to side. You can also use a level or eyeball it. Drive the screws all the way in, pinching the string with the washer. Note this pinching does slightly weaken the string, so no need to overdo it.
Step 12: How strong is it?
What is the weakest link? The bailing twine I used here will support my weight (175 lbs).
I tested the pinching system by suspending 5 gallons of water and 35 lbs of metal, which is a little shy of 80 lbs. I used a 2" drywall screw, and hung it from only one of the pieces of twine. After a day, the only visible change was that the drywall screw had sagged down about 2 mm.
When I removed the weights and tested it with my body weight, the twine snapped at the screw, indicating that the pinching does weaken it. So the capacity for a single string is somewhere between 80-175 lbs.
Step 13: What about making it fold up?
Here's one of the many ways you could make it fold up and stay up.
Fold it up and mark where the shelf hits the drywall screw. Drill a little hole next to your mark from the top of the shelf. Not all the way through!
Take your little screw (it has to be smaller than your drywall screw) and snap it so that you can screw it into your shelf and it won't poke through. Screw it into the hole you just drilled.
Step 14: Making it fold up
Place your magnet on the drywall screw.
Push the shelf up so that the little screw meets the magnet. With any luck, it should stay.
Trim the extra string.
Step 15: Shabby to chic
Possibilities are endless.