First, you need access to the Altar of Illusions. Go to the Wizard in his tower, which is southwest of your farm. You can find it on the left side of the map (mark it as a large, blue tower).
To find the Wizard, check the lower floors of the tower, but to talk to him you need to be friends with him for at least 4 hearts. To do this, you need to give him the following items:
- Purple mushroom
- Solar essence
- A miracle sheep
- Essence of emptiness
He also likes Quartz, but he doesn’t give as much friendship as the other four options. I’ll add that the Wizard’s birthday is December 17. Any gifts you offer on this day will have an increased effect.
Once you have a sufficient level of friendship, go down to the basement and use the Altar of Illusions. Stand in front of it and offer 500 gold coins to change your appearance. You can change a few basic characteristics of your character + you have the ability to change the species of animals roaming your farm.
You should have several options for your cat and dog.