Online resources for type-pairing are typically centered around whatever digital typefaces are available (free), and there tends to be a web-design bent to the information. This is all useful and worth investigating, but I want to focus on the basics of type pairing from a strictly visual standpoint. This parses a bit of what I know from classic typographic studies, a little web digging, and a lot of seeing, comparing, and curiosity.
What the experts say
Robert Bringhurst, in his splendacious volume The Elements of Typographic Style, recommends that we all learn a little history. He suggests two things. One, that the text honor its subject. If a text is about contemporary American culture, one may choose a typeface or style that reflects that time and place. If the subject is Italian history, one may choose a typeface designed in Italy by a designer of the time. Two, that we pair typefaces based on the basis of their inner structure. This is where the visual concerns begin to pile up.
Looking at a typeface like Futura, we can see that it has a geometric flavor to its design. For that reason we might not pair a calligraphic typeface with it, instead choosing another face that stresses mechanical design over calligraphy. A typeface like Bodoni
Start with one
It takes two to tango, but you've got to set the mood of the dance by choosing a type style that conveys the flavor of the subject and the clarity of the content being expressed. In many cases a single well chosen typeface will accomplish both of those things.
KEEP IT IN THE FAMILY
Many typefaces include entire families of related weights and widths. For example, Berthold Akzidenz Grotesk includes light, regular, bold and italic weights in each of three widths; condensed, regular and extended.
Know the content
In order to properly select typefaces for a given project, you must have the content in hand, and you must read it. I repeat, you must read the content and understand how the text is to be used in your design, layout, publication, or sandwich truck menu.
If you're creating the content yourself, you should have it finished or near-finished before you begin the design. You're not going to bake a cake without a recipe—the content is at the top of your list of ingredients.
For example, you're designing an editorial feature that has a title, subhead, by-line, lead-in paragraph, body copy, image captions, and a pull quote.
Create a stylesheet
Style sheets have been used for decades to spec out how a document should be reproduced. That's how The New York Times is able to reliably produce a consistent publication every single day, and it's how they are able to reproduce that same look across a multitude of digital devices. As the web came into it's own, the use of Cascading Style Sheets (CSS) created a stable foundation on which the web has been designed and redesigned over the past decade.
In a CSS file, the designer will specify any number of sizes, colors, and other information that tells the content how to behave on screen. It