Obtaining pets

Daily Quest

Starting level 10, you can take a daily quest , 3 times per day from Pet Dealer Rachel in Freedom Harbor with 3 reward to choose from :
Wolf - Eats meat, has attack skill "Weaken I".
Ram - Eats fruit, has healing skill "Self-Recovery I".
Turtle - Eats snacks, has defense skill "Possession I".

Capture

At level 30, you need to visit Pet Trainer Hicks to learn Basic Soul Catching. You can go to Creekbank Valley and capture all the pets that appear there or use the skill on same types of souls in other places. Using the skill, even when it fails, costs 1 energy.

Monster will sometimes have an icon underneath their healthbar showing they can spawn a soul when killed. They have a medium chance to spawn one. The soul is an exact replicate of the normal monster except it is in transparent blue shape. Upon using the capture skills, you get a pet stone.

At level 35, you can acquire the Tamer job to learn Advanced Soul Catching. This skill will not work on souls appearing inside Creekbank Valley, instead several additional pets can be captured. Using the skill, even when it fails, costs 5 energy.

[Ashtralana86]

I'm just starting out so I'm only level 13 but I will be looking forward to this

[Azure Mystic Flame]

A definite good start and I will help you expand more on this when I gather images and other bits of information! thank you for posting it for people curious about this.

[SendarSlayer]

Good enough, could be expanded with a list of possible pets and where to find them.