Short answer: Thank the person, give a clear answer, and offer an alternative if possible. For example: Thank you for thinking of me, but I cannot commit to this right now.
A fuller explanation: When someone asks "How do I say no politely?", they usually want more than a one-sentence definition. They want the direct answer, the reason behind it, and a simple way to remember it.
For writing and communication, the goal is not to sound complicated; the goal is to make the reader understand quickly. A strong answer usually has a clear purpose, a simple structure, and wording that matches the situation. Before writing, decide what the reader needs to know, what action you want from them, and what tone is appropriate. The best version is usually shorter than the first draft, because editing removes repetition and unclear phrasing. A useful test is to ask whether someone could understand the message in one quick read. The practical takeaway is to write plainly, organize the message, and make the next step obvious.
Simple example: Imagine explaining it to someone who has heard the phrase before but never really understood it. You would start with the main answer, then add one concrete example, then explain why that example proves the point.
Common mistake: The common mistake is stopping at the short answer. That can be technically correct, but it often leaves out the context that makes the answer useful.
How to remember it: Keep the core idea in one sentence, then attach one example to it. The example makes the answer easier to recall later.
Bottom line: Thank the person, give a clear answer, and offer an alternative if possible. For example: Thank you for thinking of me, but I cannot commit to this right now. The deeper value is understanding why that answer makes sense and how to apply it in a real situation.