It depend what you are doing. If you are writing a formal letter for example, you might address it "Dear Sir or Madam" or "To whom it may concern." If you are being formal or grammatically correct you would say something like this: "Someone has left behind his or her coat." But typically we use "their" for a person we don't know the gender of even though it is technically plural and grammatically incorrect. "Someone has left behind their coat." Also, instead of "Is he or she coming into town today?" casually we would say "Are they coming into town today?" even if it's just about one person.
As far as animals go, if it's singular and we don't know the gender we usually say "its," (or if we don't care about political correctness) "his"