Discipline training is stat building and getting skills for pet with Skill Practice. First skill you choose. I usually choose First-aid so the pet can revive me when I die. Then the next 1 or 2 skills the game chooses. When your discipline is 100% you can take your pet out. To get to this you need to train discipline. Select Pet Management then Pet Info. Then select a pet. You will see a train button just under pet image. Select it. (See images below) Then you select Discipline. Then you can select stat and skill practice. There are different levels of training. Keep it at Easy. Then select a stat and start disciplining. Also select skill practice to pick a skill and start building for skills. When you see the stamina icon green or blue with down arrow stop and wait until after your pet is hungry and fed to train more. You can use Life Potion to continue training but I prefer to wait. Save Life Potion for emergency situations. Life Potions are only given by game and should only be used in dire situations. You can't buy it or make it. Players can't give it to you either. Back to disciplining pet. Make sure you get the skills before you reach 100% discipline. I missed doing this with a Vanilla Potum I have. Only has First-aid. Maybe it'll help if you look at it like this: Leveling a pet is no different than leveling yourself. If you have a Perro which delivers a earth pounding punch you set up stats just like for knuckles. It's important to recognize what pet needs to excel in the game. I recommend focusing on these stats: str, agi and dex. If your monster uses magic then int is needed. Don't ignore vit because some pets may need this. Basically you just see what works for your pet. You can build your pet stats more when you can work with your pet out in the field by calling your pet using party feature.
Decipline tip from Japanese bloggers! I will share about a bonus buff when feeding your pet when deciplining. To stating our pet, most of us choose "easy" mode to get safe 2 potential points. If you choose "hard" mode you only have 60% chance to get 3, or else 0. But! There is a way to make "hard" mode 100% success!! Without using orb too!! Coryn club mentions about this but didn't seem to clarify on how. So here goes. Feed High grade pet food! This occasionally gives out decipline success +50%, and this is a guarantee "hard" mode 3 pt. It's a bit costly than other feed but if you have a spare spina, maybe worth giving a try.