What disc do you have? Leopard? Tiger? Either way you can connect the Hard Drive, insert the disc into the machine and reboot the machine while holding down the "C" key.
You'll come to the language select screen, choose yours. From that next page you may want to format the external (erase it all) using the utilities menu at the top, and disk utility. Select your external HD and choose erase, if it's an Intel machine make sure the formatting is GUID. APM will work also but is for PPC machines.
quit Disk Utility, continue with the install disc, as per the instructions. on the install location page select your external hard drive, continue with the install.
When it's done you should be able to boot to it using your "option" key as soon as your Mac powers on. Don't forget your updates.