Start by purchasing the correct equipment. A driving horse has a piece of equipment that goes where the saddle would go - it is also called a saddle (I believe) but is MUCH thinner (more like 4 inches versus 16 inches) with a girth. On the top of this "saddle" are 2 small circles - the reins go thru that. So you would need this driving "saddle" and 2 long (driving) reins. Also a longer whip (driving whip) - should be about 5 feet long.
Put a bridle on the horses head and attach the driving reins (removing the riding reins). Run the reins thru the saddle loops so that when you stand behind the horse holding the 2 reins they connect from the horses mouth to your arms through the loops.
Now you should use this to teach your horse to ground drive. Assuming the horse doesn't kick, and knows basic voice commends - walk, trot, whoa, walk the horse in a straight line while standing behind him. Be careful since he may spook when he sees you directly behind him - use your voice so he knows it's you and to keep him calm. The whip is tapped lightly on his butt for forward (use voice also) and for turning. Turning left you would pull l;eft rein and lay whip (no tap unless he ignores it) on RIGHT side - so horse naturally moves away from whip. Whip helps prevent horse from just bending it's head/neck when you use left rein since whip encourages horse to move body to follow head/neck.
Make certain you educate horse in BOTH directions. Do not trot until horse easily walks, halts and turns. When that is perfect add trot in small increments - about 4-5 steps in trot (think jog or you will be running hard to keep up) then walk or halt.
After horse knows ground driving you'll need to purchase the rest of the harness (headstall and leather than goes across the chest which is what attaches to what you want to pull). Be prepared if horse bolts forward OR stops dea when he first experiences weight against his chest. Best to start with enough weight to feel it but not too heavy. Also pull something you don't mind it it gets destroyed. I've seen horses panic and kick the crap out of the bogey man thing following them.