If you're wondering how to actually install the OS onto the drive in the first place:
1. While booted from your internal drive, go to Utilities folder, double click Disc Utility.
2. From the right side of the window, you can see all the drives including your external drive.
3. Select it and choose erase. Format it as Mac OS Extended Journaled.
4. After formatting the External, restart holding down "C" to boot to your Tiger DVD.
5. Install the usual way choosing your external drive.
After it finishes installing, then do what inflexion said.