How to say NO politely

Saying "No" is important. If it wasn't, the 'yes-man' would not be part of office folklore and ridicule. But some people have a really hard time saying it. And for good reason. Are you always trying to be nice to others at the expense of yourself? Or are you afraid that saying "No" might lead to conflict with your manager or the office bully?
It's time to stop the madness and pushing off important work that you need to get done. Telling people "No" does not need to be an act of rejection. And if you do it right you will not destroy relationships that took a very long time to grow.
Saying "No" does not mean that you are disagreeable or a nasty person. In fact, I believe saying "No" brings more options to the discussion table! because contrary to what you are told, it can actually prove that you are tuned in.
It can show that you are a focused listener and attentive teammate. Everyone has their own set of priorities and saying "No" means that you are respecting the person who made the request and your valuable time.
The key is to avoid what most people do: ignore the request. Ignoring requests will diminish your value and relationships faster than saying "No" more often than you say "Yes." It appears that you are not listening which is clearly disrespectful.
Some say that you should +1 everything. For example, when someone suggests that you should change your entire plan, you should say "That's a good idea and what about if we did it like this." I think this approach is disingenuous, because we all know that some ideas are just stupid.
Let's act like responsible adults who can have meaningful conversations. Successful people follow these four simple steps to assess requests and say "No" when it's appropriate.
1: Hear it
If someone asks you to do something or for something, you should assume that it is important to them for one reason or another. They likely would not ask you otherwise. It's your responsibility to get to the heart of the request and why it matters. Working towards understanding ensures that you will clearly see what the person making the request sees and you will be able to gauge how important it is to apply energy against it. And total immersion in the request for even a very short period of time tells the other person that you value them and what they are trying to achieve.
2: Goal first
If you are going to make good decisions and say "No" when needed, you need a way to assess the requests. While most requests are easy to quickly answer, some require meaningful investments of time and energy to satisfy (e.g. put together a new email campaign or research a new market opportunity). You need to know whether you are going to invest that effort. And to do so wisely you must establish a “goal first” approach and a true north for where you are headed. A "goal first" approach is about defining your vision. Because If you do not have a vision, it will be difficult to understand what major requests are aligned with your goals and your direction and need your attention longer term.
3: Yes or No
You should respond to requests quickly as they come in. That's because you can not afford to keep revisiting them and the person making the request does not want to wait. You need to quickly analyze them as they are received and allow your "goal first" strategy to guide you. Most requests can be quickly handled but the goal of a rapid "Yay" or "Nay" should not be at the expense of accuracy. There is no point in being hasty but wrong. It is absolutely ok to acknowledge that the request was received and that you will get back to the person shortly. The key is to digest the information and its importance as quickly as possible so you can get on to the next one and creating more value.
4: Be transparent
Allow someone to peak inside and understand why you responded the way you did rather than just hearing your response. Explaining the "why" makes the "what" simple to digest. You need to be more than just nice because being nice alone does not help someone see your perspective. This is especially important when saying "No." The benefit to you is that if you share your assumptions and motivations and they are wrong -- the other person will have a chance to help you see a better way. If you simply provide your answer and when pushed respond with "My mind's made up", you will avoid ever having to change your course, but you're limiting your opportunity for growth.
Now, let's be real. There are times when you must say "Yes" even to what appear to be silly demands. That's how hierarchical organizations work. Sometimes you follow orders because other people know what's best for you and the organization.
If your boss asks for something that is difficult to deliver, sometimes you will need to say "Yes." But you should also explain that you are working on A, B, and C and would be happy to move something out to get the request done. Ask for guidance when the priorities are not clear.
Successful people learn how to say "No" to requests based on a framework that helps them assess value vs. effort. Saying "No" to more requests is one of the biggest favors you can do for your organization and yourself.