The Fox Trot 
A correctly performed  fox trot will have a bit of a "pause" between beat 2 & 3. 1-2--3-4. This is because the hooves set down closer together in diagonal pairs than they do in lateral pairs, with the fore hitting just a bit before the diagonal hind. This makes the Fox Trot an uneven 4 beat gait, diagonal in timing. 
To begin let's look at the horse and rider configuration. 

 
 

The horse's back will be carried in a slight dorsiflexed position

The Horse

• The horse will be in a slightly more dorsiflexed body frame in the Fox Trot compared to the Flat Walk or Running walk., but not to the extent required for a Trot. 
• The croup will bob up and down in rhythm with the gait.
• Overstride should increase from the walk, the degree will depend on speed and conformation of the horse, overreaching or disfiguring the front tracks.
• Long, reaching step in front and a quicker, higher step in back, with the tail carriage of a horse bobbing when the rear foot passes the break over point. The movement of the front hoof should be smooth and set down as the completion of an extension of the shoulder and front leg. 
• The head nod will be very noticeable with head motion in time with the reach of the rear hooves.
• The horse should be moving in a rhythm which can be described as having the same cadence as "a chunk of meat and two potatoes".

• The rider's position should be in the base position, with the pelvis in the Neutral pelvic alignment, until you need to make adjustments that will influence the horse's gait.

Female Pelvis, Base Position.

Rider in Base Position with Good Equitation for Fox Trot.

The horse who has already been trained to perform a correct Fox Trot will increase his reach and overstride, as well as the speed at which his legs move. You should hear a 1-2--3-4 cadence to the footfalls. The horse's head and neck will nod up and down in rhythm with the motion of his shoulders, back and legs, using his head as a counter balance to the movement in his croup with the saddle balanced at the pivot point. 

Increasing speed, reach and overstride at the Fox Trot
For a horse to increase his speed at a Fox Trot requires that he have a flexible and strong back to be able to take increasingly longer steps when pushed on for speed. It is therefore very important that you are not interfering with the horses use of his back. 

Sometimes it is necessary to encourage the horse to improve their Fox Trot. 
Suggested Reading 
 
 

Always make sure you are sitting in a balanced seat, allow your body to move with the horse, keeping your lower leg slightly behind the girth. Think of what it feels like to stand on the bow of a boat while you hold a glass of water in each hand. The waves cause a gentle rocking of the boat. Absorbing the waves in your hips and waist while your upper body remains quiet and your hands independent, keeps you from spilling the contents of the glass. This is similar to the feel of a Fox Trot in which a back to front rock in the saddle is felt by the rider, but the hands remain still but supple to aid the horse in  maintaining the rhythm and animation of the Fox Trot. Uneven rein contact and artificial “Pumping” of the rein can result in loss of impulsion. 

Exercises
 
 
 

Achieving Response, Gait and Confidence through Relaxation

Rider Affect on the Horses Movement

MAKING CONTACT How to use a bit 

WORKING The WALK

Exercises at the Walk

Conditioning a Horse to Gait

Equitation for Gaited Horses

Exercises for Increased Flexibility in Gaited Horses

The Seat and getting the horse on the bit.