I haven't tried it yet myself, but I noticed a nice-looking iPad app called "Typography Insight". Looks like it's aimed at folks who want to learn the basics.
Developer's site:
http://www.typeinsight.org/
A review at The Atlantic:
http://tinyurl.com/3szx6qt
Well, I notice in the promo shot above that the category under the finger, Egyptian/Slab Serif, is not actually exemplified by the typeface shown/named, Century. So much for “insight.”
Or maybe the finger is just trying to point out the error?
Captured from web.archive.org on 22 Oct 2013. view this capture