I saw that people level up really fast. How do you guys do that?

There are a few ways:

1. Fastest is probably the Riding Hall, where you gain one level after 4 hours, at the cost of some silver and all the energy of the pet (this is the reason why you should lower its' energy to 0 first.)

2. Items: Energy Drink + Insight scrolls, then manually battling the highest Exp giving pet you can win against. (Here is the link for the exp table, along with some formulas.)

Agreed. But I would recommend manual leveling until level 20 and then proceed with the riding hall. On lower levels, you are able to gain multiple new levels in one fighting session.

@Wireath The riding hall doesn't cost any energy to use; my pets have always finished training with the same amount of energy they started with.

Other items that help with XP gain are stimpacks and aromatic beans but they are more difficult to come by since they're only available during certain events. Stimpacks double the rate of energy regeneration for 3 days. Aromatic beans last a week and raise the max energy by 5.

@Lytala -- Really? I remember it dropping energy to 0 before, guess I remembered wrong then.

Oh yeah, there was also an event item that automatically leveled your pet too, forgot what it was called though.

I think that one was called a transmitter.

I battle all of my pets, then the ones I want to train faster I send to the riding hall. Also, I recommend building a sanctuary so you can freely increase the energy of one pet to 10 each day. :)