The rhythm of the horse is the foundation. This is established when the horse can maintain a rhythmic, steady tempo within its natural four gaits. The walk is a 4 beat, the trot is a 2 beat and the canter is a 3 beat. The horse needs to be neither to fast or to slow and moving through the back to the front in a relaxed, supple way. The rhythm must be established first. Each step of the pyramid builds on the one before it.
Suppleness is the looseness and flexibility of the horse's body. It can be longitudinal and lateral. Longitudinal suppleness is the ability of the horse to stretch his top line forward in a relaxed manner reaching into the bit. Lateral suppleness is the amount of sidewards flexibility to make a round circle or move sideways.
Contact is the horse's acceptance of the rider's aids which include the seat, legs and hand. Good contact is shown as a happy horse moving freely forward on the aids and willing to accept the bit. The poll will be at the highest point, the back will be swinging and supple, the jaw relaxed and the nose slightly in front of the vertical.
Impulsion is seen by the amount of thrust the horse has coming from the haunches to the front. The hind end engages and the horse has the desire to move forward energetically reaching well under his body with his hind legs. Impulsion is accomplished naturally when the first three stages of training are solid. It is light and forward.
Straightness is an important phase of the training scale. A horse is straight when the hind foot tracks in the hoofprint of the front or slightly beyond. To achieve straightness the horse must be equally developed and trained on both sides of its body which means going in both directions, right and left. All horses have a stiff side and a flexible side. They will tend to do things better when traveling on the flexible side. It is like us, we are either right handed or left handed and are awkward trying to do things with the off side. A straight horse is a happy horse. It has the ability to do what you are asking with less chance of injury or evasion.
Collection: the ultimate goal of classical dressage. This happens when all parts of the training scale have come together and are solid. It happens naturally. A forced collection is not fluid. When the horse has the strength to collect, the forehand lightens and you have self carriage. The horse is not leaning on you and is truly carrying its rider in harmony. You now have all phases of the training pyramid working as one unit.