The best way to do this is to boot up from your OS X installation disc. When you go about doing the installation just choose the external HD as your installation path.
You want to make sure of a few things first. If you don't know how to boot to your system disc, when powering up your machine hold down the 'C' key and quickly insert the disc.
Also, you want to make sure your external drive is formatted correctly; When booted to the system disc look in your menu bar for Utilities > Disk Utility.
You will see your external drive in the list. Click on external drive (not the partition of the drive) and what I normally do is just erase it and give it any old name. Make sure you choose Mac OS Extended Journaled. (this is in the erase tab in disk utility).
Quit Disk Utility and go on with the installation.
When the installation is done you will be prompted with the welcome screen and setup. If you want to boot to the external drive in the future, you can do this by holding down the option key on boot. This is called the option manager. You can choose to boot to anything that is connected to your computer that is bootable such as an external drive or optical media.
Hope this helps and good luck!