This might seem complicated, but I promise once you figure it out it's very easy. I learned this when I was a kid in elementary school. We made coasters.
You have two options for your loom board. Cardboard or Wood.
Wood - Pros: Sturdier, the work can be tighter, you can use it for years if you want.
...........Cons: Weighs a lot, possibly more expensive, harder to cut to size, harder to cut slots.
Cardboard - Pros: It's free everywhere any size, lightweight, easy to trim, if you make a mistake it's easy to replace.
..................Cons: It can bend with too much tension, can get soft in humidity, pets like to lie on it and chomp on it.
Whatever size rug you want you need a piece of cardboard a couple inches larger. Refrigerator cartons are great for large rugs. EDIT: I forgot to put pizza boxes here! They're great for making large placemats or small bath mats.
Next you need to think of the size and characteristics of your materials. I was talking about using old sheets and t-shirts in an earlier post so I'll use that as the gauge. It's best not to use a stretchy fabric for the vertical strips. It's easier to use something that won't keep stretching as you work. I often used cotton twine or slender rope. I've even heard of people using plastic grocery bags.
So, we want the verticals to be non-stretchy and about 1/2" to 1" wide continuous strip. The horizontals can be anything material or sizes you want as long as they are at least as long as the board.
PREPARING THE LOOM
As I'm talking about this I'll refer to the side with the knot as the top. The vertical strips as verticals and the horizontals as horizontals.
1) Cut slots at least 1" apart and about 1 1/2" deep on both long sides of your cardboard. FIG-A shows the slot cuts. If it's a square just make sure it's the opposite sides. You can do a circle but that might be too complicated for now, if anyone is interested I can make directions for that but once you see how this works you'll see how a circle would go.
2) Tie a knot in one end of your non-stretchy continuous strip. Push it firmly into the end left-hand slot. The knot should be at the back of the board. Draw the strip down the front of the board to the bottom slot and through it to the back. Then pull it across the tab and back through the next slot toward the front again. FIG-B shows the back of the board. FIG-C shows the front. Make this as tight as you can without bending your board. If your strip is too short just tie another length on it and continue. When you reach the last slot tie a knot at the back of the board.
The material you use for the horizontal strips can be any width as long as they are as long as the board to avoid loose ends in the middle of your rug.
Weave them one over, one under, for the tightest weave. Note FIG-C. After you have two or three done push them toward the slotted edge of the board to tighten and make more room for others. Continue this until your rug is completely filled in.
Clip the center of each yarn where it crosses the tabs in the back of your board as in FIG-D. After a few are clipped pull them from the slot and tie the first on to the second and the third to the fourth as tight as you can without messing up the edge of the work. If you only cut 6 or 8 at a time it prevents your work from becoming crooked due to the uneven tension. That takes care of the loose ends that were at the top and bottom of the board. The sides can be tied the same way or you can even run a seam across the ends of the rug just in front of the last vertical if you want to make sure it's secure.
EDIT: Simplified Instructions: scroll to the bottom for that thread.