I started this game, finished the tutorial and then never went back on until now. I figured out how to increase intelligence and feed my pet, but I can't seem to figure out how to increase happiness? I'm on mobile so the menus are all messed up.

you can give your pet a minion to keep their happiness maxed out, or use toys to increase their happiness one point at a time. playing with a toy uses it up, though, so there's not really a reason to use toys unless you're doing a major drills quest that requires it.