I usually start training for the lengthened trot on long lines. I say lengthened not extended because first you want the horse to get the idea of going faster with longer strides. They can do this best without pulling a carriage. Choose a verbal cue and remember to use it only for the intended purpose. I use trot up. By long lining you'll be able to see how much your horse is lengthening as opposed to speeding up. If you just get speed take a gentle feel of your horse's mouth, a light half halt while encouraging her forward at the same time. ALWAYS release the bit pressure immediately! Ask again until you're getting the response you want.
When you're ready to work on lengthening the trot while driving, choose a part of the ring and ask for the lengthening in the same spot until you can see your horse drop and stride out. Drop? you say? You will be able to see your horse's back lower as they reach out in a longer stride. I use a breath to stiffen my back to ask for a slow down or halt. It helps the horse halt squarely and at the exact point you want.
Any green horse needs time and work to build up muscle for lengthening and collecting. Keep that in mind while working your horse.
I drive in American Driving Society competitions that call for three trots - working (medium pace), slow or collected, and strong or extended.