Have you noticed that grammatically correct phrases are sometimes not quite natural for native speakers? I'm sure you have. Vice versa, real communication can sometimes generate grammatical nonsense, but this nonsense is more adequate to the situation that any other grammatically irreproachable phrase. Here is my favorite example from the real Russian communicative practice.
In Russian, we often ask questions with negative particles; however, the meaning of such questions is positive. These questions are actually not of the “don't you?” kind. They are something different. When your Russian friend asks you “Ты не видел мою книгу?”, you should not be confused with the mention of “не”(don't) here. In English, this question is just “Did you see my book (anywhere here)?” Another example: “У тебя есть эта книга?” and “У тебя нет этой книги?” are absolutely equal questions (Do you have the book?) despite the obvious grammatical fact that the first is positive and the latter is negative. “Не” here is closer translation of “by any chance” than to “not”.
So why “не” (not)? Here, the negative particle does not negate anything. Russians use it to make their questions a bit more polite; so as to be not so pushy. It's like saying “I'm sorry for disturbing you with my question” or “I'm asking you about this just because I suppose you could be helpful, but you are not obliged to help me, so please feel free to say no”, but way shorter. The negative particle in the questions like these leaves you room to refuse or deny something in a non-offensive way.
How to form not-questions? Just add “не” before the verb, or use “нет” instead of “есть” when asking about having or not having something.
When to use “не”? Well, it is not necessary. You may ask questions in direct way. But if you want to improve your speaking skills to the level of a native speaker, you may add “не” any time you feel unsure if your interlocutor can answer your question or when you want to show that you wouldn't mind a refusal in the response. Please note an intonation here. The pitch increases on verbs; same intonation as any other simple questions.
Photo by Colin Kinner