Transitional serifs have a stronger contrast between thick and thin strokes (examples include Bookman, Mrs. Generally speaking, Old Style serifs such as Bembo, Caslon and Garamond will combine well with Humanist sans serifs like Gill Sans and Lucida Grande. 'Serif' and 'sans serif' are very broad classifications, and each can be split into several sub-categories.
You can use a single font and adjust the weight, the size or the colour. This applies even if you're not pairing fonts. You also need to establish a clear hierarchy in your font pairings: what will be the purpose of each one? Which will be for display and which for body text. For example, if you have a really unique display face full of personality, you'll need something more neutral to do the hard work and create a balance. It's important to balance personalities in font pairings too. Our mind ends up confused – is this a different font or not? Good contrast is often provided by pairing a serif font with a sans-serif font. For example, overly similar serifs or similar sans serifs don't tend to look nice next to each other. If typefaces are too similar, it's likely that they'll conflict.
Contrasting fonts can be hard to find as you're effectively searching for two fonts that are different but also complement each other rather than causing conflict.
