Optima is a very famous typeface. It's probably the most famous humanist sans --- these are faces that try to capture the quirks of handwriting or calligraphy. The uppercase letters mimic carved-in-stone Roman letters. Because it has serif-y features (flared terminals in particular) it's notoriously hard to harmonize with other faces. Every designer in the world can spot it on sight.

In general, look at the contrast in weights (where do the lines get thinner and thicker) and the axis of those contrasts (is the "hand" drawing the letter positioned at an angle?). In a Sans, you can also eyeball how "geometric" the letters are; is the "o" a perfect circle, for instance?

Even if you're not a designer (I'm definitely not), it's worth it to buy a copy of Bringhurst's _Elements of Typography_; it's a beautifully written and designed little book.

Getting to know typefaces is much like getting to know any other visual art - some distinctions are highly visible and obvious (modernist versus baroque, punk versus techno) while others are more subtle (folk-pop versus folk-rock) due to the general shifting and swirling of aesthetic trends.

If you're really interested in identifying typefaces, get at least conversationally familiar with the technical terms for different parts of letterforms: serifs, bowls, counters, shoulders, etc.: http://www.fontshop.com/glossary/ Look at instances of typefaces you see around you, try and identify the different parts and see if any of them are particularly notable.

Some of the more obvious things I've learned: The bowl of Palatino's P doesn't quite meet the stem, unlike most other serif faces. Optima's strokes have a gentle concavity to them, unlike most other sans-serif faces. Gill Sans tends to be wider than the Platonic sans-serif face, and the tips of C and G are sliced off with a vertical stroke, leaving quite pointy terminals behind. Helvetica's most famous birthmarks are the surprisingly complete tail on the lowercase a (compare to Arial's a) and the surreal curly tail on R.

Of course, some typefaces are even more subtle than that. If you showed me Baskerville and Times New Roman, I could probably tell you which was which, even if I couldn't identify Baskerville on its own. Distinguishing between the hundreds of typefaces in the Bodoni/Didot genre is way beyond me.

Anyway, if you want to learn more about typography, I heartily recommend picking up a copy of The Elements of Typographic Style by Robert Bringhurst - if you're a practicing graphic designer, it's got lots of useful information; if you're not, it's a book by a typographer with decades of experience who also happens to be a well-known poet, writing about something he's passionately interested in, so you know it's going to be a good read.

Typographers can tell. For others, there are sites such as http://new.myfonts.com/ and http://www.identifont.com/identify.html. I own a printed variant of such a tool: the book "The Typefinder". Far from being an expert, I do not know whether it is any good (google learns me that it has a foreword by Frutiger, so It cannot be really bad), but I find it entertaining and educational. Among other information, it gives the most distinctive characters for each type, with arrows and dotted lines pointing out what to look for.