The horses I buy are already trail horses, but I still “polish them up” a bit.
I get blue, black and silver tarps, lie them around the round pen and first hand walk then ride the horse over them. You want a trail horse to walk over anything.
If you can, create a muddy spot somewhere and walk your horse through.
If you have access to cavaletti (jumps will do), start walking your horse over them, gradually raising the cavaletti. I’ve seen quite a few horses balk on the trail because they didn’t understand how to walk over a large branch, or they try to jump. Personally, I don’t care for jumping obstacles but some people don’t mind.
Hand walk your horse on the trail, start by just walking them a few feet outside the property then walk back in. I do this a few times even if a new horse is good about leaving the barn.
I go on several trail rides following another horse(s) who knows the trail and is calm.
Repeat each process until you feel that your horse is comfortable with them. Good luck and have fun on the trail!