Question about Pet Skills

Hello!

My name is Juuno and I'm new to the game. I have a quick question:
In regards to the pet skill, I do realize we can teach them one skill, and the rest will be randomly learned. How will the pet learn a new skill, is it through just leveling up or would I need to do pet fusion?

Your input is highly appreciated, thank you! ><

EDIT: This question was already answered. Thank you so much!