If you know how, or can get a trainer to help you - ground -driving... everywhere.
Handy... lateral work - in hand.
Essential - yielding body (shoulder, ribs, hips... separately) with very light pressure.
The softer you have your horse to your hand, and body the easier it will be to transition to the cart.
You can also, if you have harness for him, have him drag a lightweight drag, or even plank of wood.
Try to introduce the closed bridle before he goes off - some horses seem to object a bit to them at first.
And voice training... a lot of driving has to do with verbal communication. We talk ours up all the time... both praise and corrections as well as cues.