Analyzing a well-designed page usually starts with typography. You can always determine the fonts used on a web page by looking at the site's CSS, either directly, or through Chrome Developer Tools, Firebug or similar. If you only want to know the font (or simply develop your recognition of typefaces), digging through CSS can be a little arduous. As an alternative, I would suggest three tools:

The WhatFont tool is a Chrome extension that can bring up the font used on a web page with a mouse hover. It includes information on stack selection, style, weight and line-height, and includes support for TypeKit and Google Web Fonts.

Font Finder is a similar plugin for Firefox, while Fount is a bookmarklet that does much of the same thing in any browsers.

If you have more suggestions, please add them in the comments!