How do I use Split View in OS X 10.11 El Capitan?
It appears that I was doing it wrong.  I don't see a way to enable split-screen from just two fullscreen windows in mission control.  Nor do I see a way to enable it from two regular windows.  But if you have one fullscreen window and one regular window, you can drag the regular window onto the fullscreen in mission control, and it will create a split-screen view.

I tried this successfully with Safari, Finder, and Chrome.