Assuming that you have Windows and Ubuntu 12.04.1 installed and running smoothly on your computer, the best method might be starting Ubuntu 12.04.1 normally and upgrading to Ubuntu from within Ubuntu 12.04.1.
If your system has not already asked if you would like to upgrade, you can run "Software Sources", switch to "Updates" tab, and make sure that "Notify me of a new Ubuntu version:" is followed by "For any version".
Then your system will prompt you to upgrade to Ubuntu 12.10, or you can as well start "Software Updater" manually to make this happen instantly.
Using a live CD/USB for this purpose for such an upgrade might be the second option, while a fresh install can also be considered as a third option (to replace the current Ubuntu version, for example).