How familiar are you with the complex plane?
It helped me a lot to be explained quaternions starting from the complex plane. More specifically, by constructively inspecting their properties. There's a great interactive article that gets the pedagogy of teaching such a complex concept (pun definitely intended). Unfortunately, I can't seem to dig it up.
I recall the author's blog using all kinds of CSS and/or WebGL trickery to make 3d backgrounds – anyone know which blog I'm referring to?