This probably looks confusing but to do the Loom Stitch you need to understand that the beads are not woven onto the loom. A thread above and another below a row of beads holds that row of beads on.

To do the Loom Stitch first get a loom and string it. Then, use a long, long line of thread on your needle. To start and end, tie the thread to the loom strings.

Put the beads onto your thread in the pattern your design calls for in that row.
Place the row of beads under the strings of the loom. Push the beads up and carefully work the beads through the loom strings with one bead between each string. There should be final strings on the out sides of your row of beads.
Keep the beads in place with your hand. Be sure that you are pushing the beads UP through the loom strings and that the holes of the beads are exposed above the loom strings.
Bring the needle and thread back through your row of beads, keeping the needle and thread above the loom strings.
In this way you have a thread above and a thread below the loom strings.

How do you get a loom?
Easy. Make it out of 1x2's, a couple metal screws, eye hooks, and bolts.

What do you do if you make a mistake? Don't worry about it. Mistakes in beading add uniqueness to your project but if it's a mistake you can't live with you can do one of two things if you catch it quick enough. If you have one or two beads too many on the string you can take a needle nose pliers and crunch the bead. Pieces fly everywhere so watch your eyes and only do this with small seed beads. Or if you have several beads you want to remove hold the row between your fingers and slide the beads back over the needle. If you put the needle through the beads you can catch the thread in the needle and you'll be in a mess of trouble.