How to Say No at Work
Most people say yes first and figure out the problem later.
That reflex is exactly what gets you buried under tasks that were never yours to carry. Saying no is not rude, and it does not make you a bad teammate. It just means you checked your calendar before your mouth made a promise.
The steps below cover how to pin down a request, word the refusal, offer a smaller yes, buy time, handle repeat askers and deal with the guilt that follows.

Name the real request first

You cannot answer a vague ask. When someone says "can you handle this," ask what "this" actually involves: how many hours, what deadline and who else is involved. A colleague who asks you to "just review a deck" often means a full rewrite of forty slides by Thursday.
Once the real scope is on the table, the conversation changes. You are no longer refusing to help. You are looking at a specific job with a specific cost.

Say no to the task, not the person

The wording matters more than the answer. "I can't take this on" lands differently than "I don't have time for you." Try: "I want to help, but I can't do this well by Friday."
That sentence keeps the relationship and closes the door. It also puts the limit on your capacity, not on their worth, so the other person hears a scheduling problem rather than a judgment. People accept a full plate far more easily than they accept a rejection.

Offer a smaller yes if you mean it

A partial yes often works better than a flat no. If a manager drops a report on you at 4pm, you might say you can send the first section tonight and the rest Monday. That is a real commitment, not a brush-off.
Just be careful. A smaller yes is still a yes. If you offer it and then quietly resent it, you have solved nothing and added a grudge to your week.

Buy time before you commit

The easiest way to avoid a bad yes is to delay the answer. "Let me check my schedule and get back to you after lunch" is a complete sentence. It sounds cooperative and it costs you nothing.
Use those hours to look at what is already on your plate. If the new task pushes a deadline you already promised, that is your answer. Managing up, which means working openly with your boss on priorities, works the same way. Tell your manager what would slip if you took this on, and let them choose.

Watch for the repeat asker

Some people test your boundaries once. Others test them every week. If the same person keeps handing you work you never agreed to, one polite no is not enough. You need to address the pattern.
"I noticed I'm picking up these requests regularly. Can we talk about how they get assigned?" That moves the issue from you versus them to a process problem, which is where it belongs.

Handle the guilt that follows

The discomfort after saying no fades faster than the resentment after saying yes. Think about the last time you agreed to something you did not want. You probably spent the whole task annoyed, and the work showed it.
A clean no protects the quality of what you have already promised, because your time goes to the work you agreed to do. That is not selfish. That is the job.
You will not get this right every time, and that is fine. Start with one small no this week, on something low stakes that you would normally absorb without thinking. Notice what happens. Usually the ceiling does not fall, the relationship survives, and you get an hour back.