In addition to the external drive that will host your Windows installation (the 'destination drive'), you will need another USB drive (the 'driver drive') to temporarily store the Boot Camp drivers. I found that certain operations failed more frequently if I used the USB hub in my monitor. Throughout the process, directly connect all devices to your Mac.
I tested this process on a MacBookPro11,1 running OS X 10.11.5 (15F34). Here's an updated procedure for Windows 10, based on orkoden's excellent answer.