I don't recommend upgrading to Feisty before it's ready (though I've done it already myself..) and if you can, use a fresh install rather than apt upgrade (works better). Anyway, here are instructions that seem to work more or less well:
http://onlyubuntu.blogspot.com/2007/...to-ubuntu.html
Lower on the page somebody says it'd be better to use the GUI method, but I myself used apt before discovering that and I've faced no major problems so far, except those that are due to Feisty not being "ready" yet.
It takes some time to do the upgrade; my downloads took something like 15 minutes, but installing and upgrading the packages took more time.
EDIT: note that if you use the GUI method described in the page and abort the upgrade before it's ready, next time you run the graphical tool to do the upgrade it might tell you that you first need to finish a previous upgrade and tries to start upgrading your system back to Edgy. In this case simply drop off the graphical way, open a terminal and use apt-get; another option is to revert the upgrade process completely, which means at least changing every "feisty" into "edgy" in apt's sources.list file to prevent the GUI application from doing anything stupid.
Note: after a few days of using Feisty after an upgrade there seemed to be some conflicting packages (two that tried to overwrite the same file) which lead me to run some fix-installs with apt. Upgrading the kernel made my wireless card useless, so I'm using an older kernel at the moment that I luckily have spared; there are other reasons for that too, but wireless is one thing that works in Edgy but not in Feisty yet (for my card, a Broadcom laptop wifi-card).
If you like playing around with stuff like that, go ahead, but if you'd like to have a system to work with, without interruptions, wait until next month when Feisty is officially released.
