Generally speaking, おねがいします is more polite than ください. For example, when you want to request some water in a restaurant, you can say 「みずをください。」or「みずをおねがいします。」. But the restaurant waiter would not say　「このbillにサインをください」. That sounds too straightforward. Instead, he would say 「このbillにサインをおねがいします」or some politer variations. When you want to request some service or intangible thing, おねがいします is easier to use. e.g. おなまえを　おねがいします。May I have your name please? でんわばんごうを　おねがいします。May I have your phone number please? よやくを　おねがいします。Can I make a reservation?

Not much. おねがいします is a little more formal than ください . Other than that they are interchangeable. By the way, there are a number of "request forms" in Japanese that range from the very casual to super deferential. Just keep on studying step by step and you'll get it eventually.