You can download the latest version (or previous versions) of Ubuntu from www.ubuntu.com and you save the file to your hard disk. It will be a file with the .iso extension which means it is an exact copy of the disk.
An ISO image is not just a copy of all the files on the disk. It is actually a bit for bit copy of exactly where those 1s and 0s are located on the disk itself. Simply copying the file will not work because each individual 1 and 0 needs to be placed in the right place. For that you need software that will burn the ISO image to disk.
You will need to use software to burn it to a disk but for some reason Windows doesn't make it particularly easy for you. If you are working on Windows, you can download a free tool that will burn an iso image to disk. It's called ISO Recorder and you can download it from here: http://isorecorder.alexfeinman.com/isorecorder.htm
If you are already using Ubuntu, you simply right click the iso file and select Write to Disk (it's so much easier on Ubuntu :)
If you're willing to pay the postage only, Ubuntu will send you a disk. All of the installation disks can be used as a Live CD as well.
Once you have the Live CD, you can boot up your machine with the CD in the drive and it should boot into Ubuntu and display a menu of options. If your machine simply boots into the old operating system, most likely your machine is set to read the hard disk before the CD drive. You can change this order by going into the BIOS.
Normally when the machine boots you will see an option to press a function key (typically F2) which will display a program called the BIOS (Basic Input Output System) and that allows you to do various machine level changes. Be very careful because you can cripple the machine by making wrong choices... Find the option that says which device is read at boot up and make sure the CD is above the hard disk. If you are worried that you have done something wrong, you can exit without saving anything and your machine will be unchanged.
With the CD searched before the hard drive on bootup, the machine will read the Ubuntu disk before getting to the hard drive.
I hope that's of some use to you. There is plenty of further information on the web especially on the ubuntu forums.