I always look at E, R, M, O letterforms to find the distinguishable characteristics. Of course, you have to have a resource to reference after that. It's been a while since typography class, but I still sort of remember the type families, and typefaces that belong to them.
Back when I was a technical writer, I spent way too much time learning about typography and even trying to do some "fine typography" on the computer, without much success. But in these days of email and web sites, I find that it's just easier to accept whatever default font the s/w offers and move on.
My favorite typeface is Caslon, and I have used it for years for projects as diverse as manuals and web sites. Designed in the 18th century and still fresh and relevant in the 21st.
Bembo and Futura are among my favorite. My first typography mistake was setting an entire chip data sheet (8 sides) using Futura as the body type and Futura Bold Extended for heads. Can you say "unreadable?"