Its actually very easy. You can train an English trained horse to a western trained horse no problem, because the western way is much more natural for the horse. Should you want to train your horse the other way, you will face great difficulty.
To change an english trained horse to a western horse you first have to change your own attitude towards riding. Instead of control and discipline you go for fun and friendship. You make your horse want to do what you want to do by letting it have the choice.
Lets start by mounting the horse. The most important thing: it doesn't matter, how you get on the horse! That's one of the fundamental rules of western riding. Do what is comfortable for both of you and don't do it by the book.
Once you sit on the horse, just relax. Stretch your leg away from the horses flanks and get rid of the broom stick you were taught to have in your back. Just sit naturally and comfortably.
Leave the reins loose. It doesn't matter, if you use one or both hands for the reins, just (again) hold them in the most comfortable way.
To get the horse going, you do not hammer your heals into his sides.
You move your hip forward and click with your tongue. The horse will feel encouraged to go rather than pushed to go.
Enjoy the horses movement! Lean back in your saddle. Dont tighten the reins.
To go from walk to trott to canter you do just the same thing: move your hip, click your tongue.
And sit back and be relaxed.
To turn right, all you do is move your hand (or hands) that is holding the reins over the horses neck to the right, without pulling his mouth.
To turn left, move your hand with the reins to the left.
To stop or slow down, you gently pull in the reins just enough to let your horse know, what you are asking. This is the only bit that takes a bit of training. Mainly, because, being used to the English way, we become all tense and afraid to loose control over the horse, when we dont have the tight reins. But western riding is all about being relaxed, and sending tiny signals through your mind and body to the horse. The horse knows exactly how we feel. So, when we are tense, the horse gets tense as well, and the last thing a tense horse wants to do is slow down. So, train yourself to be relaxed, and TRUST your horse. If you trust him, he will trust you.
A famous book I once read by Henry Blake told about a guy who was asked to train a hypersensitive, nervous horse and make it calm. So this guy took the horse, and went straight out into the middle of a parade of people with drums and guns etc. The same horse, that he was riding for the first time, stood still in amongst all this noise, as his rider put down the reins and lit a cigarette. And that the secret: he completey relaxed himself, so the horse felt, there was nothing to be nervous about and relaxed as well.
So, remember the basic rules for western riding:
1. do what is comfortable and dont follow any strict rules.
2. be relaxed. That includes your whole body; your back, legs and hands.
3. trust your horse
4. treat it as a friend and not as a slave.
Now, enjoy yourself and have fun...