So you are prepared to assume a new position at a new company, but what should you do to make the transition away from your old job as smooth as possible? Do what can be termed as the common sense stuff and you will be able to leave on the best possible terms.
First, never burn any bridges: you never know when you might require help or information from your former company again in the future. Let the company know in advance, before your actual date of leaving, so that they can start looking for a replacement. Also, let them know why you are leaving (you have to be as honest and tactful as you can when it comes to this), and do thank them for giving you the chance to work there. Do resolve any unresolved workplace issues, like outstanding work, and let other departments know that you will be leaving soon. If possible, create a list of essential tasks for your replacement, to make things easier for anyone to take over your job.