For crossing obstacles it is best to start teaching your horse at home in a controlled area. I will teach horses, either from the ground or the saddle, to place their feet where I ask. You should start with an easy obstacle and for simplicity we will discuss it from the saddle.
You have to understand the horse wants to be left alone and no better time for that then when he is doing what you want. We have to know our cues and release the horse from them as soon as they respond correctly, otherwise we become nags and the horse will decide he can either move and be nagged or stand still and be nagged. He will usually pick stand still, unless he chooses the third option which is to remove the nag.
So, to start this lesson you need to decide exactly where you want your horse to cross your obstacle. The more specific you are the easier it is for the horse to figure it out. You will keep both his eyes facing that spot no matter what. You apply your 'go forward' cue and release that cue as soon as the horse takes at least one step forward. The longer it takes the less you look for, you may need to release on his thought forward which could simply mean he does not go backward.
You will counter aid all other movements. He backs you apply go forward, he goes left you turn him right, he goes right you turn him left. As long as he has both eyes on the spot you want to cross you leave his head alone. Try to apply the 'go forward' cue when he is thinking about going forward. He shows this by lowering his head or perhaps pawing. Reward all correct responses with words and/or rubs.
When the horse actually touches the object, allow him to inspect it. For water, let him paw; crossovers, let him feel it; step ups let him try one foot at a time. An important thing to know is the first 'step' may be big. If it is and he clears the obstacle, turn him back and start from the other side. If you can it is best to work with an obstacle the horse will not feel he can jump across and an area large enough to allow you to be safe in maneuvering your horse. Repeat the procedure from the other side and continue to turn back until the horse crosses quietly.