Not all horses naturally have a slow and flowing or fast and flat stride but with a little time and patientce you can teach your horse how to collect and extend his stride.
The collected trot
In a collected trot the horse engages his hind quarters while collecting his forehand. He shortens his stride creating a round gait that is slow with plaenty of impulsion.
A rider asks for a collected trot by encouraging impulsion with his/her legs while at the same time, holding it back with the hands by keeping pressure on the bit.
The extended trot
In an extended trot the horse lengthens his stride creating a fast and long trot.
To ask for an extended trot the rider must encourage a forward motion through the legs while letting the impulsion flow through the forehand.
Collected and extended canter
The collected canter: With the same principals of a collected trot, this is a slow rocking for of the gait.
The extended canter: Like the extended trot, the extended canter is fast and long.
An excercise to accomplish extension and collection
A good excercise to do at both a canter and trot is to extend down the long side of the arena and collect and make a circle in 2 corners diagonal from each other. Alternate between laps of all working trot/medium canter and laps of collection and extension.