The posts about desensitizing in the arena or round pen are right on, however there are some other things that will help as well. Going with another horse or two who are experienced on the trail is a good idea. Get them to go through simple obstacles at first, such as crossing a small log, or crossing a small creek. Be very careful about choosing your battles at first, because if you can't get him /her to go through the obstacle, you have lost ground and the horse learns it can avoid things it doesn't like by balking and turning. Sometimes a horse will go through something it sees another horse go through, whereas you would never be able to get him/her to cross alone. Later, when you've taught him/her that you are in command here, he/she'll trust you more and will go through things alone. Pick you battles well at first, but once you have picked it, do not relent. Keep urging him/her forward until they do it.
You may need to learn how to use spurs (there is a break-in process with these for you and the horse, by the way) so you can get him/her to keep going forward. Horses (and consequently riders) almost always get hurt while going backwards. If you can keep them moving forward, you will likely come out ok in just about any situation.
Once you get the simple things out of the way, you can begin to do harder things, like wider, deeper water crossings, jumping logs, walking through fallen tree branches, jumping ditches, or jumping down drops, and steep grades up and down. Horses can do amazing things safely. Much more than most riders will ever have the guts to do.
I disagree with the advice on avoiding or riding past things that scare the horse. Whenever my horse finds something to shy at, I immediately turn her toward it and speak to her in a gentle high tone, like speaking to a child, and say, "What is that, girl?" I keep repeating that while urging her forward with my heels and keeping her head pointed at it with the reins. I keep her facing the object until she walks up to it (sometimes takes a while) and sniffs it and relaxes (licking lips is a good indication of relaxation). My mare has a high flight response, and occasionally I still get a surprise as she shys at something, but she doesn't bolt anymore. My mare has learned to trust me, to the degree that when she shys, she immediately turns toward the object, stops, and begins to cautiously move toward it, sometimes without my urging. Her fear is now turning to curiosity.