Ubuntu 12.10 has been released. You can obtain a copy here
To update / upgrade to Ubuntu 12.10 can be done in 3 ways. Via the command prompt, update manager, or using the Ubuntu CD / DVD. This guide walk you through all 3 options.
Always backup 1st. Any time you upgrade an OS (Operating System) things have the possibility of going wrong. This is true no matter if you're using Microsoft Windows, Apple Mac OS, or even Linux (Ubuntu for example).
For many people, it will be a lot easier to simply us the update manager.
Update Manager Upgrade
Press Alt+F2 and type in
Update any current packages
Reboot if required (if rebooting, go back to step 1 when done)
Press check again
If not updates are found, it is now safe to click on UPGRADE in the top right and allow Ubuntu to automatically update things from here
For others a command prompt maybe easier and allow more customization during the upgrade. This will also be helpful if you're needing to upgrade remotely (server for example).
NOTE: If you're doing this remotely, odds are good that you're already logged in as ROOT and can drop the SUDO command. If not, you'll need to keep this "as is".
Terminal Command Prompt Upgrade
Install the update-manager-core package if it is not already installed:
sudo apt-get install update-manager-core
sudo apt-get update && sudo apt-get upgrade
CD / DVD upgrade
You'll need to be using a computer which can boot up from a CD or DVD. Boot up using it and Ubuntu will give you the option to upgrade.