I've pet sat for a friend's two dogs before. I would have the pet owner (before they leave) write what I call "puppy instructions". These tell me how much food the pet(s) need, what kind of play the dogs are used to, favorite toys, any medication or supplements, how and when the pet(s) are fed, how often the pets need to be let out, health info of the pet, and any idiosyncrasies that will help the pet(s) adjust.
I would also recommend that you meet the animals you will be pet sitting and the environment in which I will be pet sitting for them in. (I've only done pet sitting while also house sitting). Meeting the pet(s) in advance will help the pet(s) get used to you.
