I made a post a while ago about how to saddle a dragon. I recently remembered that, and another question came up: how to pilot a flying animal?
Land animals tend to run in the direction their heads are pointing, but an animal flyer may well look to one side and keep flying forward. So, as I see it, reins are useless(mainly because my characters lie on the animals, they don't sit, the link has an answer that convinced me to make this change); besides, they can irritate the animal and you don't want to annoy an animal that can make you free-fall from the clouds to the ground or devour you or attack with fire (dragon) or lightning (thunder bird), for example. The way Hiccup pilots Toothless would only work for an animal that has a long tail with a part missing. Depending on the turbulence, the wind will prevent the animal from hearing the pilot tell which direction to go.
Note: it has to be a method that doesn't use magic, so even those who don't have magic can pilot a flying animal.