Pet nurturing stupid questions...

I'm wondering how often you can nurture your pet and have it count towards leveling up and/or earning a pet token. Is it once a day? Any time they're not full green rings on all the buttons? Does it have to go to empty first? Can anyone walk me through it? I want to level my pets, but it's a boring task so I hate to do it and have it not count! I can't quite seem to find a clear answer by googling.