The USDF has written this great article to help spectators better understand dressage, as well as what they can do to help be a good spectator.
Like any sport, watching dressage is more interesting the more you know about it. Dressage tests used at shows are divided by graduated levels, from the most basic walk/trot to the Grand Prix test that is the same test that is used in the Olympics. The tests are divided into separate movements, and the judge gives a score for each movement. The score sheets are then totaled to determine class results. It will help you understand what is going on if you can get a copy of the test you are watching, plus here are some additional thoughts:
1. Less is More
In dressage, the less you see the rider do, the better, because that means he is communicating with his horse quietly and his horse is attentive — they are working as a team.
2. Good Figures
Circles are round and lines are straight, a precept true in geometry and dressage. A 20-meter circle should go from one side of the arena to the other, a 10-meter circle only half way across. A horse should not weave on a straight-line movement.
3. Tempo and Rhythm
Rhythm is the repetition of footfalls. A sound dressage horse has only three correct rhythms – a four-beat walk, two-beat trot, three-beat canter. Tempo is the speed of repetition of strides. Every horse should have a consistent tempo throughout the test that is controlled by the rider, a tempo so obvious you could sing a song to it.
Horses, like people, have good days and bad days and days when they are just feeling a little too good. Naughtiness in horses can be exhibited in bucking, rearing, tossing of the head, or even jumping out of the dressage ring.
During a test, the horse needs to remain calm, attentive and supple. If the horse gets tense, he gets rigid through his neck and back, which can exhibit itself in stiff movement, ears that are pinned back and a tail that swishes constantly and doesn’t hang arched and quietly swinging.
6. Rider Seat and Position
The rider should sit upright quietly and not be depend on his whip, spurs or voice to have a nice test. Riders who use their voice have points deducted off their test score for that movement.
7. Whipped Cream Lips
When a horse is relaxed in his jaw and poll (the area just behind his ears), he releases saliva, you might see white foam around his lips and mouth. That is a good sign as it means he is attentively chewing on his bit and comfortable in his work. The amount of white foam varies from horse to horse.
8. Horses and Flight
Horses have two main mechanisms for protection from danger: they run and they kick. Remember to always allow plenty of room for the horses at a show and never approach any horse without first alerting the rider that you are doing so.
9. Scary Stuff
Horses have the strangest aversions: plastic grocery bags can remind them of Satan’s minions and an opened umbrella can cause bolting to three states over. Again, use caution at horse shows and think before you toss away noisy garbage, open an umbrella or put on and take off plastic rain ponchos or blankets in the stands.
Focus is important during any test, from Training Level to Grand Prix, so remember to be courteous and follow the rules by staying about 15 meters (45 feet) feet back from the competition ring and remaining as quiet as possible during rides. If you have any questions about where you may stand or sit, check with the ring steward.