Here's how I'd do it. Bear in mind that my advice is worth exactly what you paid for it, and that you should back up anything you care about before you start.
1. Edit /etc/apt/sources.list and change all occurrences of "dapper" to "edgy".
2. Issue the following command: sudo apt-get update && sudo apt-get upgrade
This will download and install a lot of packages. Be patient.
3. Issue the following command: sudo apt-get dist-upgrade
The reason I use two commands - upgrade and then dist-upgrade - is that I have found in the past that a straight dist-upgrade causes pain.
4. Install the "deborphan" package : sudo apt-get install deborphan
5. Clean up old crap: sudo orphaner
6. Reboot to pick up new kernel.