The Western Horse's mane is not braided at all. It is either banded with light colored banding rubber bands or beaded with what is called "pony beads" available at hobby stores in all colors of the rainbow and more. Banding rubber bands and a banding tool are available at Tack Stores or Catalogs.
If anyone has seen "speed beads" around a horse's neck hanging just in front of the withers and chest. Those smaller round beads are "pony beads". There is also "rythum beads" used on Saddlebreds or other gaited horses in training sessions to help the rider get in rythum with the horse's movements. The "rythum beads" have bells threaded in them.
If the horse in that picture is an Arabian or Arabian cross I would guess that is why the mane is not pulled and banded like you would normally see. It goes against breed standard to pull an arabians' mane. For lower level shows you would have to check the rules, but around where I am, they don't give penalties for not having the mane done a certain way. I'd check the rules for which ever shows you are planning on and see what the consensus is.