ください is connect with te-form of verbs to make a sentence a request/order. ください alone means "give me". This is a polite way to ask for something, as Anthony-san wrote. e.g. この本をください。 (Please give me this book. In the book store, "I'll buy this one.") e.g. この本をよんでください。(Please read this book.) お願いします means like please be kind to me or please do me a favor. This doesn't connect with a verb. We often use with よろしくお願いします to make a request politer and show your will. Sorry if this is not what you are looking for. この本をよんでください。よろしくお願いします。Please read this book. I would appreciate it. はじめまして。よろしくお願いします。Nice to meet you. Please be kind to me. And as Anthony-san mentioned, お願いします can be used like "please" instead of a verb when the request is obvious. The meaning of たのむ depends on the case, but in general it means "to ask". たのむ doesn't create a request or order form. If you could share an example, that would be helpful. Here' are my example sentences. 明日でんわしてほしいと、友だちにたのんだ。I asked my friends to call me tomorrow. 先生に、10分だけ話したいとたのんだ。 I asked the teacher to give me just 10 minutes to talk with him. 「明日、その本を貸してほしいんだ。たのむ！」 "I would like you to lend me the book tomorrow(I need your book tomorrow). Please!!" (casual only)

I believe ください and お願いします used when you are asking for something. (Requesting for something) e.g. お茶ください "Tea please", こちください "Come here please" お願いします is more formal, or use when the request is something you cannot do yourself . e.g. 水をお願いします (Water please) 東京駅までお願いします (Tokyo station please (to a taxi driver)) I'm not sure how to use tanomu at all, but I hope I helped with the other two.