I answered your barrel training question on your other thread.
As for trotting and loping -- You ask them when you have prepared them well enough that they are ready. [Another book would be required to teach this to someone that has not done it before or assisted in helping a good colt started do it.]
I thoroughly believe in ground driving. I do not think a colt will ride any better than he drives. When I have my feet on the ground I can control him better than when I am a passenger. So, I teach a horse to guide (to follow its nose), to go forward into a walk and a trot when I smooch and slap the reins on his rump and teach him to slow down and stop when I pull on the reins. If the horse has a lot of 'forward' in him, I teach him to back up on long lines. If he lacks forward impulsion, I do not back him up and spend a lot more time getting him to go forward over and around obstacles. Some, I drive across fallen logs, over creeks, up and down hills -- just about anywhere I will ride in the first few rides.
I find that the more I ground drive one, the less traumatic the first rides are. I like it when I get on for a first ride and the colt rides like he has been ridden 2 or 3 times already.