Before you do this, make sure that you are really sure that you want to remove Ubuntu 11.10. You will loose all files that you have not backed up. If your intent is to keep all of your files, but upgrade Ubuntu to this newest version, simply run Update Manager from your existing Ubuntu 11.10 installation, and choose to upgrade to Ubuntu 12.04. Update Manager allows you to easily upgrade to a newer version of Ubuntu while keeping all of you files. If you are sure you want to remove Ubuntu 11.10 instead of upgrading, proceed with the instructions below.
To remove Ubuntu 11.10 from your computer to install Ubuntu 12.04, you will first need a Live Cd or a Live USB. After you boot into it, select Try Ubuntu. Then, you will need to open Gparted, and delete the partition that Ubuntu 11.10 is installed on. Then, you can install Ubuntu 12.04