After the initial green horse training, where your horse learned to wear the harness and has been ground trained thoroughly, you might want to continue on to teach him to go in front of a cart. By now he has learned to back up safely into shafts. How to teach him this, see here.
The green horse should be about 3 years by now and for the last 6 months being schooled regularly and be perfectly doing the basics.
Best is to use first a cart, not a wagon. Make sure all parts are in good working order!
Exercise in a paddock and have got an experienced helper, who holds on to a long lead rope that is fixed to the horse's bit. He should be there only for "emergency cases", not for leading the horse.
Make sure that the blinkers are correctly fitted for your horse. It can be scary for him, if he could see you mounting onto the vehicle and "growing" tall all of a sudden.
By making the vehicle carefully heavier after a few lessons, he will learn to manage plus weight and be able to deal with altering states of balance.
Then practice turnings and backing up with the cart. Show him different surfaces, esp. tarmac. Some people even draw zebra-crossings, arrows and other road markings onto their practice-grounds, just to help the horse to adjust to these markings.
If he is able to do all this without problems carry on to the next step in this green horse training program is to put him together with an older, experienced driving horse.
In this stage he will learn to go in the right pace, the older horse will either pull him on, or keep him back in the right speed and pace. He will also learn how to turn safely to the left and right. Often green horses might "lean" against the experienced one. This usually disappears once he has learned to balance himself in front of the cart.
Very important is to train him to go slow. Try to avoid letting him trot or gallop as long as he is a young and inexperienced horse
Practice little and often rather than only at weekends and then for long hours. Too long breaks in between lessons (if they are a few days apart from each other) will mean that you always will have to re-start.
The goal for a lesson should be successfully reached in this one lesson, so try to teach in little, and easy digestible steps. Work with patience and take the time.
If we want a horse to respond, we have to adapt to his pace. So give him enough time to "digest" what you teach him during a lesson.
The whole process of training a green horse will take a few weeks to break him and after that roughly about 12 months until he has learned everything properly. Consider to teach him during all four seasons.
If the green horse is trained like described above and goes securely in front of the cart, you might want to go ahead and train him on the road in public traffic.
For these lessons be welcomed to read on here.
More Tips on Horse Training
Green Horse Training, Part 1