^ The above has covered that. Let me run you through a basic layout of a general lesson at my barn.
Everything, and I mean EVERYTHING, she starts us out with "Okay, now pick up a BIG and STRONG posting trot!" to get the horses stretching.
Then generally, it's some speed transitions, going to the middle and doing lateral work (Haunch turns, sidepassing, forehand turns, leg yields, etc.)
That's just a general thing. There is always the incorporation too for the individual student and their goals. Like for me my past few lessons have been a lot of practice picking up leads invisibly with my green horse because it helps me think about it more when she's giving me instruction rather than me doing it on my own, and having that extra set of eyes helps.
This is my trainer with two of her students...lol Corey on Tammio who is a pretty solid mare and Amber on Maija who is three years old.
And then this is her with me and Amber, back when Selena was just starting to lope the barrel pattern.