[erdevs]

"Mastery can only be achieved through practice."

Try saying no to smaller things first.

Also, to get over the natural (for many people) social anxiety involved in saying no, try saying it a different way. Example: "Okay, I'd love to do this. Help me prioritize here, though. I've presently got to do X,Y, and Z. I can't do a good job with all 4 and stay on time. Should I cut X? Wait to tackle this? What do you think is best?"

Eventually you'll work up to speaking up and creating preventative measures. Eg "if we're going to frequently face interrupt-driven task priorities, we need to move to some Kanban-like and also give up on concrete milestones."

But yeah.. just start trying. Practice makes perfect. As long as your not a jerk about it and take care to explain yourself and not make a requester feel dismissed, nobody will hold saying no against you. (Unless you're just not as productive as others, or unless it's a crappy environment/culture, in which case you should bail if you can.)