briskly, quickly
happily
obediently
Anne trotted obediently beside her mother.

across, along, back, off, over
He trotted off to greet the other guests.

down, up
She trotted quickly down the stairs.

Trot is used with these nouns as the subject:
horse, pony

brisk, fast
gentle, slow

break into
When the horses reached the field they broke into a brisk trot.

slow to

at a trot
We set off at a fast trot.

into a trot
He kicked his horse into a trot.