Well... I'm just a western trail rider, never been to a show or event in my life. But my general rule of thumb is to control the horse the same way you do from the ground; with your whole body.
Like what Scout said, just put more weight into the direction you wanna go, keep eyes up and use the subtle changes in your body to cue your horse before leg and then rein.
At least that's the method I've used for three years, and it hasn't failed me yet