The foxtrot is a four beat diagonal gait. What this means, is that each leg moves independently (four beat), with the diagonal pairs moving close together. The rhythm will be 1-2, 1-2. Much like the hard trot, the more suspension (the pause between each “1-2”), the rougher the gait will be. The foxtrot is unusual in that it is the only gait, four beat or otherwise, in which the front hoof lands first! The Missouri Foxtrotter is of course expected to have a foxtrot, but any horse that has both a true trot and any four beat gait can probably also perform the foxtrot. Unlike most four-beat gaits, I prefer the foxtrot to keep the pairs moving closer together, to avoid the tendency of the horse to lean forward onto the shoulder in this gait.
Front Right-Left Hind–Left Front-Right Hind
Or
Left Front-Right Hind–Front Right-Left Hind


The the rider’s hip motion in the foxtrot is mostly forward-back. A horse in an “extended” foxtrot may give you just enough movement to post to. It you feel like you could post to it without a lateral wobble, but you still hear four beats, you’ve found the foxtrot. Now relax a little and let your hips just follow your horses back. If you post strongly in a foxtrot, you will encourage the hard trot.
Further reading:
Missouri Fox Trotting Horse Breed Association
“Within a Fox Trot” by Liz Graves