Depending on the horse introducing trot poles might need to be something you need to do very gradually! I had a pony that took to poles [and jumping!] like a duck to water and needed no "gradual" about it because he enjoyed it so much. I have a friend who has an Arab gelding that was TERRIFIED of poles when she first got him, to the point where she couldn't get him close in the beginning. He is now a competitive 2'8" eventer, showjumps 3'+ [not sure exactly how high] and is continuing with his dressage/show hack career.
One thing you can do if they have that extreme fear is lunge them over poles, particularly in a round pen where they can't escape the issue. Pressure and release is VERY important in the fearful horse - you keep it on if they are standing still or backing away but the MOMENT they so much as shift their weight in the direction you want it to go you back off. Timing is everything.
Once your horse is comfortable with a line of poles on the ground I like raised poles [like 5cm off the ground tops] to help encourage the horse to engage the hind and lift through the back. It also encourages the horse to be ok with taking higher steps to clear the poles, and can be great position-building for you as well. If you can sit, post, or ride in jumping position through a line of raised poles [or poles with alternate sides raised, which is even better] while keeping a strong position, you're a better rider than me. I can't even sit the trot through ground poles.
The step after the raised poles is to drop them all again and turn the last pole into a small cross. Ends about 1' off the ground works well, I find. You just trot through the line again and again until the horse forgets it's there, then gradually remove poles from the line until you have just your fence and a canter pole one stride out. The canter pole will help with placing your horse in a good takeoff spot.
THIS is when you ask the horse to canter. At the beginning of your horse's jumping career it should never be jumping fences without a good ground line because a ground line helps them calculate how high they have to jump. Once your horse is very confident, you can start playing with false ground lines.
From your little cross you move up to a very small vertical, maybe 1' high if that.
At your LOW HEIGHTS, once the horse is confidently cantering up to and over the fence and getting away without breaking rhythm, you start playing with "fills" and scary things. Once your horse is ok with verticals at a certain height, play with the setup. Create oxers. Put a tarp under the jump and splash it with water to create a small "liverpool" fence. Hang things off your standards and poles, hang carpet or cloth over your fence to create a "solid" fence.
When you have done everything you can think of, trained fill, all different types of fence, ridden courses in a balanced and calm manner, you can put your fences up ONE HOLE, starting with the verticals and once the horse is fine with the height moving to your oxers. Keep up with the fill training, change your course with every session, get the horse used to being surprised.
One jumps training session a week is enough generally speaking but there is nothing wrong with popping your horse over a fence or two at the end of a flat session especially when they are still learning. It keeps it in their minds that way.
Take the time it takes, so it takes less time.
If your horse rushes, BACK TO BASICS. If your horse refuses, BACK TO BASICS. Run-outs are RIDER error, not horse error. Over-jumping means they need MORE time at that height or lower, not that they want to go higher.
I have seen very well-bred beautiful natured honest horses turned into lunatics by being pushed too far too fast [a particular A-grade showjumping stallion comes to mind, consistently throws honest get but the man himself has a real dirty stop to him]. I have wrecked a horse that would have been a fantastic jumper if he'd been given the time to grow more confident. I trained a pony and ended up with something that consistently got in TOO deep and had to pop his fences... lucky for both of us he was really scopey and could clear a 3' vertical from really really bad spot from a TROT, and this pony was all of 12.1hh.
Be careful and make sure you do this working with a coach. It's far too easy to ruin a talented horse's career because you got excited/over-eager/impatient/whatever and pushed it too far too fast. You can't progress a horse too slowly and in fact if you take more time it takes LESS time.
The other thing is, have YOU done much jumping? I hadn't, when I started teaching my first horse [the one I totally ruined], and I've already told you where that ended up... if you haven't done much jumping it's best to learn on an experienced schoolmaster before you go about training a youngster. They can do some pretty hairy things when they're learning [I had a horse jump 4' over a 1' fence once!] and if you're an inexperienced jumper you compound the balance issue, you will make mistakes at some point like jabbing on the horse's mouth [I still do that sometimes, my boy is a schoolmaster but not an easy ride and I do occasionally get left behind], and you probably won't be able to stay on if your young horse does something silly, as young horses do tend to do.
Before I even START jumping a horse there are a few things I like to have:
w/t/c balanced, round and soft, swinging through from behind and always on the correct canter lead
basic laterals [leg yield is REALLY useful in a jumpoff]
REALLY good stop and steering - you shouldn't have to use the reins in your stops/turns on the flat
really good transitions especially walk to canter [walk-canter builds the right muscles and will assist with flying changes]
flying lead changes are essential in competition above 3' heights, I like to have a horse that will perform flying changes on a figure-eight before I start jumping but smooth simple changes are better than nothing - no more than 3 strides of trot through them
----- THE BIG ONE: reliable on trails [for me that's huge, I do a bit of eventing and don't want a horse that's going to have a heart attack at its own shadow, or a leaf, or a kangaroo]
You may find, especially if this horse is off the track, that you're working on the flat for a year or more before you so much as take it over a small cross. Jumping is beneficial to dressage training so poles/cavallettis are fine from day one but any actual jumping, I find is best left until the horse can at least perform a decent Level 1 dressage test. Level 2 or 3 is better.
A CLEAN SLATE FOR THE FUTURE