KEEP IT TO YOURSELF
Don't tell your work colleagues until you have told your line manager. If your employer comes back with a counter offer, it could be embarrassing.
Unless you particularly want to upset your employer, don't just announce your departure. Give them the required amount of notice (check your contract) so that you don't leave them high and dry without anyone to cover your role.
CHOOSE YOUR MOMENT
Asking your boss for a quick word to explain the situation is fine, but be sensitive to the fact that they might be too busy. Wait for a time when they have a few minutes to spare so that they can concentrate on the news you're about to give them properly.
DON'T BEAT AROUND THE BUSH
When delivering the news, be direct and polite. Don't start with a massive preamble.
Try something like: "I've been considering my options here for some time, and I've decided it's time for me to move on. I'm very grateful for the opportunities I've had here, but I must hand in my notice as of today."
PREPARE FOR QUESTIONS
Your boss may want to know more about why you're leaving so be prepared to answer those questions. If they value you, they may even offer other incentives such as a pay raise, increased benefits or a promotion to convince you to stay. So make sure you have considered whether you are prepared to stay and, if so, what it would take to keep you.
BRING A COPY OF YOUR RESIGNATION LETTER
It's professional to provide your boss with written notice of your resignation.
SHAKE HANDS, SMILE AND THANK YOUR BOSS
Even if you can't stand them and never want to see them again, try to act with dignity and respect. Once you've done this, you can tell whoever else you want.