So what should you look for? A principle issue that gets overlooked when pairing fonts is contrast: make sure that they're noticeably different. The key word is noticeably, and some of the following methods will help you pair up different fonts with enough difference to help readers discern one piece of text from another.
Mixing Classes, Qualities
If you were to combine Times and Garamond, the two serif faces are so similar that no differentiation would be evident. However, if you were to combine the serif Times with a Clarendon from the slab serif class, the two are different enough to create a sense of contrast. Moreover, they also have a different weight. Times looks lighter than Clarendon. Other combinations would include pairing a slab serif with a sans serif, script with sans serif, or sans serif with serif.
Consider Weight, Case, and Spacing
If you're not sure about what fonts to pair, just look at the differences in weight. Using a heavier font as a headline or subhead will help create a sense of focus. The text could even be set in a different case, either all caps or small caps, to create further differentiation.
Contrasting Styles in One Font
If you are limited to one font and need to create typographic variety, consider how many variants the font has. A face like Myriad Pro includes roman, bold, condensed, and italic styles of each of the preceding three. With Myriad Pro alone, a designer could create enough differentiation to layout an entire book that would include headlines, subheads, body text, captions, and food notes. Myriad Pro is just one of the many fonts that has this breadth. Others, that have been included in software packages such as Adobe's Creative Suite, include Adobe Caslon Pro, Minion Pro, News Gothic, and Helvetica Neue.
Make All of the Details Different
Lastly, with the right amount of control, you can set a document in more than two typefaces, provided you spread the differentiation around the document. Whether you follow this principle or any other, keep the golden rule in mind when pairing fonts: make things noticeably different.