how can i train my pet?

Simply, there is a training centre at Veta Lake Riverside (you can see all the pets on the gym)

Alternatively, there's a great comprehensive guide here in the Battle forums :)

[edit] Sorry for the error earlier!

If you want to navigate there for any reason instead of following a link, Jim's Gym is not in Veta, it's in Riverside.

Battling is pretty complex even with the guide, so ask away either here in Help & Questions or in the Battle subforum if anything is confusing.