Pet usually gains 200 experience points every 2 minutes when it's summoned. So it's just a matter of time, you can just stay with your pet up, and it gains exp. In some locations like Club, Nemesis and Suer, or using some buffs, it gains more exp.
Remember to take a look to pet sceen (default Y button) from time to time, because you need to click UPGRADE every 5 levels of pet, when it grows up changing the apparence. If you forget to upgrade, it stops at that level till you don't upgrade it.