To get your first Zentia, talk to Tammy in Mulberry Village.
Using the pet allows you to use Autopath to the next destination. Click on the Blue Underlined Text in a quest to acquire an Autopath destination. View the Pet Skill Bar to see what skills are available for your pet to use. Click on the Green-Square icon next to the Pet HUD to have your pet lead the way for an Autopath to your requested destination.
Clicking on the "Pets" Icon in the lower right hand corner of the screen, or simply pressing the [N] key brings up the 'Pet Management' window.
Here you can Summon, Recall, Feed, Release, and Rename your pet. You can also view their skills and progress.
After you finish the quests necessary to move from Mulberry Village, you will be taken to Serene City, where you can first meet Monster Hunter Jen. Talking to this NPC will allow you to learn the Monster-hunting skill and Processing skill. In the same area, you can talk to Pet Trainer Chao to train your pet.
Monster-hunting is a public skill which can be learned by everyone and won't impact other skills. You can use this skill to capture various pets. They can improve your ability and accompany you in your traveling!
After learning Monster-hunting, you can buy the Monster Mirror from the grocery dealer Jack Lo in Serene City. Equip yourself with the mirror and you can capture monsters and beasts. When you put your cursor on the monster or beast, a small textbox at the lower right corner will pop out. If it writes Tamable, then you can capture the target by using the Monster Mirror. The lower the target's HP is, the higher the chance to capture it will be.
You attack a monster to make it weak, then, attempt to Capture Monster by using your skill (pictured).
Most monsters will have the word "Tamable" in their description which appears on the right side of the screen when passing the mouse over it. These are the monsters that you can capture once you acquire the Capture Monster skill. You are only able to capture up to a certain level monster according to your skill level. You can increase your skill level by capturing more monsters to rack up experience and improving your ability through Monster Hunter Jen.
After capturing a pet, you'll get a pet egg which needs to be identified by the Grocery Dealer. Click the Grocery Dealer and you'll see two options which are Zentia Gold Identify and Identify All. Click any of them to identify your pet egg.
Processing skill allows you to change the identified pet egg to Devil Essence which can be used to feed your pet (and mounts). Feeding your pet can improve its Mood and Loyalty. When the Loyalty becomes zero, the pet will run away. So please don't forget to feed it!