Takes them a while but you need to make sure they are walking forwards correctly in walk first, by this I mean right at your side, so there shoulder is is just behind yours, making sure they go straight into walk when you ask, once there forward thinking in walk, trot wil come once they understand what your asking.
Clear voice commands, a lunge whip (in some cases) is useful, hold it in your left hand, just to tickle/gentlye flick on the back of the legs legs (more like swish) and a little tug on the head coller and say trot on, once they go, let have 5 paces and then lots of praise, you'll only have to use it a few times and they will soon get the idea, and will soon learn with your voice command and by your body language when you start to run.
My daughter taught her then 2 yr old pony to trot up by just playing every day, usually to and from the field.
One day she just said to me, watch this mum, and off they trotted together.
Think it took less than a week to master it properly. And im convinced it was so easy because the pony saw it as just another game with mummy (they play a lot of games), no pressure or stress.
Good luck