So you've got a new job, and you've got to leave your current one. There are a few things you need to do before up-and-quitting:
Make sure you tell your boss first. Your direct supervisor should be the first to know. It may be tempting to talk to your close friends and colleagues, but hold off because word spreads quickly.
Give at least two weeks' notice. The old adage of giving two weeks' notice may actually be required by your company. If you're in a higher-up position—you're senior management or you supervise a lot of people—it'll be harder to replace you, so give three or four weeks' notice.
Thank your colleagues. When you thank them for being a fun bunch to work with, use the opportunity to leave your contact information. Your colleagues are your network, and you never know when you may need them for a reference or a job in the future.
Document exactly how you do your job. Your successor will thank you for it. Within reason, offer to keep in touch to help acclimate him or her to the job.
Don't slack off. No matter how tempting it is to come in late or leave early in your last few weeks at a job, work as hard as ever. You don't want your last few days to leave a bad impression on your coworkers; that may come back to haunt you later.