After that's done, you'll need to edit your software sources list. If you're using the Gnome desktop environment, type in the following:

sudo gedit /etc/apt/sources.list

This will open up your sources list in Gedit, the Gnome text editor. If you're using Kubuntu, you'll want to type in the following:

sudo kate /etc/apt/sources.list

This will open up your sources list in Kate, the standard text editor for KDE.

Once opened, you'll see a number of lines that look similar to this:

deb http://us.archive.ubuntu.com/ubuntu/ feisty main

What you'll need to do to ensure that you upgrading to gutsy is replace every instance of "feisty" with "gutsy" which will point your package management software to the newer Gutsy Gibbon software repositories. To do this the easiest way is to use Replace (Search -> Replace).
After this is done, there are only three more commands necessary:

sudo apt-get update

This will update your software repositories, enabling you to upgrade your system. To do this, type:

sudo apt-get upgrade

This upgrades any and all software packages already on your computer which can simply be replaced. There will be, however, some software packages that require new packages to be installed alongside them, and some which require an old library to be deleted and a new one installed in its place. To do this, simply type:

sudo apt-get dist-upgrade

This will complete the upgrade process. Now all you need to do to experience the wonderful, unstable gloriousness that is Gutsy Gibbon is reboot your computer and log back in. So enjoy, and if something breaks, don't say I didn't warn you!