You said you don’t have restore discs but I imagine regular OS install discs work the same way.
I put restore disc 1 in the slot.
I held down the option key while turning on the computer. This allowed me to select the DVD drive/restore disc to work off of.
I used This Guide from Western Digital (although I had a 1TB Mac-formatted iomega) to make sure the external drive was partitioned correctly.
Due to differences between WD’s version and what I was seeing I wasn’t able to follow the above note for note but I was able to get through the partitioning process.
Once that was done, I initiated the install process. Along the way I chose which drive to install the OS on and selected the external.
After installing I selected the external as my startup volume.
There’s probably something I didn’t do correctly because I have to click through a disk eject message whenever I boot up. Small price to pay, though.
I contemplated replacing the internal myself but chickened out and looked into making an external work instead. And by Jove, it did!