how does evolving work?

The guide on this site will help but essentially, you need a brand for that pet, like brand of kaze to evolve chika and so on. You can apply the brand whenever, you don't have to wait and then you master both it's skills using orbs of mastery. Make sure your pet is fully awakened to level 250 and then level your pet up to 250. Once you've completed all these steps, give them an orb of evolution.