It's a very easy process and you won't mess it up. Print this post out if don't have access to another machine.
Remove the external hard drive from your Mac first. The disk you want is #1 which contains the utilities and installer. Insert that disk, reboot the machine and hold down the C key as soon as you hear the bong sound. Continue holding it until it begins to boot from the disk.
Once it boots, accept the license, and English as the language. Don't proceed with the installer but instead go to the top menu that appeared. Click on Utilities, and then on Disk Utility. Now highlight your hard drive on the left side. Highlight the line that shows the disk capacity (GB).
Click on erase and select the format to use: Mac OS Extended Journaled.
Name the hard drive MacIntosh HD
Click on erase at the bottom of the screen, then click erase again on the second window. The drive will be formatted and ready to use. After this is done you can proceed with the install of Leopard 10.5.X. You should then be asked if you wish to transfer data from another Mac. Reply yes and attach your Time Machine backup and then select OK. Time Machine will restore your data and apps.