This is the first time I am trying to write a "how-to", but I thought I would give it a shot. So here goes nothing.
Peyote beading is fast and simple. The only thing you need to remember is to skip one, use one.
You start with a bead, any size, on a thread. The thread has to be flexible and fairly thin as it has to pass through the beads at least twice. In addition, you need to have enough beads, you are probably going to use more than you think. The number of beads has to be uneven, but you can decide how many.
So, start with a thread and a bead. I have used an elastic thread. I also prefer to have the beads I am going to use in a small bowl next to me. If the beads are very small, I prefer to have them on a bead cloth. But for this beading, the beads are large enough that I prefer to have them in the bowl.
In the next picture, I have added all the beads for the first line. In total 6 beads, two purple, two pink and the last two purple. Notice that the thread is long both also in the end. That is because you will use that thread when you connect the bracelet.
Here I have started on the second line. The thread is passed through the number 5 bead on the first line.
Here I have added another bead to the second line. I hope you can see the rhythm. One bead outside another, the thread through the next bead, and then another bead outside the another. So in this picture you will se the top two beads are tighter, then there is one single, and then there are two together again.
Here I have added the last bead on the line. It looks a bit shaky at the moment, partly due to the fact that I have used an elastic thread and partly because it always looks a bit shaky when you go down. Notice that there are only three beads in this line, so half of the original number.
Here I have started the third line. The bead I have added is going to lay next to the first bead on the first line. The thread then goes through the last bead on the second line.
Now it is starting to come together. When you bead upwards, the beads are falling more into place and you can easily see if you have made any mistakes. So here you see that I have added a pink bead after the purple bead and now they are starting to form a nice line. It is easy to see where the third bead on this line is supposed to be.
Here I have finished the third line. It looks like there is only two lines when you look at it like this, but remember that you have first gone up (the first beads), then down (the second line) and then up again. So there are three lines.
Here is a picture of the line 4, going down. Now you can clearly see where you are supposed to place the beads in the next line. It gets easier once you finish the first lines as it is easier to see the pattern.
Here I have completed the 5th line, going up. Again, the pattern is perfect when going up and you can see what it will look like in the end.
Continue like with the same pattern, bead one, jump one, bead one. You decide how long the bracelet is going to be. When you reach the desired length, you need to end on top. Then you place the two edges together and you bead in the same pattern, pulling beads from both sides, until you reach the middle. Then you take the thread that is hanging loose from the first bead in bracelet, and use that to connect the beads from the bottom up to the middle. Then you tie the two threads together in the middle, tight with a surgeons knot or what suits you the best. You can add a bit of glue to the threads if you are worried that the knot may slip.
Then you will end up with something like this:
Good luck with your beading! Remember to try out different patterns, different lengths and colours. The good thing is that you can always cut the thread, pick the beads apart and start again if you are not happy with the result.