Example beaded by Rosemary Ighel.
Even count flat peyote is super easy, and I use it a lot for bracelets, necklace and other things. It's basically a form of netting, but with only one bead spaces making a very dense fabric.
Start by stringing the number of beads you need for your start row. Look at the pattern, and start with an "up" bead.
Add the first bead of your next row, and go into the second bead of the first row.
The beads in the second row push the beads in the first row into the staggered position you see in peyote, sort of like bricks.
The next rows are worked the same way,switching directions.
Animated this is how it works, the beads are seperated so you can see the thread path, in peyote stitch it's actually very tight.
To zip up the sides if your design is oriented horizontally instead of vertically, or to close up the bottom, you can "zip" the beads together as long as you are using an even number of rows.
The same technique works for the sides of brick stitch if you want the structure of brick.
Check out my personal site
for free graph paper to graph out your own design.
For the bracelet pattern above, and several other peyote stitch patterns, check out my index
You can also do short tubes zipping up the ends to make little beaded beads, or adapt a lot of brick stitched patterns to even count peyote. It's a fun way to make amulet bags too, instead of beading a tube, you bead a long strip, then join the sides with brick stitch.