string pet = "Dog";
PetType petType = (PetType)Enum.Parse(typeof(PetType), pet);
int petValue = (int)petType;

PetType result;
if (Enum.TryParse<PetType>(pet, out result))
    return (int)result;
else
    throw something with an error message

(PetType)Enum.Parse(typeof(PetType), pet)

PetType petTypeA = (PetType)Enum.Parse(typeof(PetType), "Dog");