Well, the primary way was always looking at the brightness (the apparent magnitude) of the star. If it should dip suddenly, then it's *possible* that it's part of a binary system. We've detected a couple by looking at the amount of light they emit...

Suppose there's a big star, and it has a smaller companion star, both shining, but the larger star is much brighter. We can detect the amount of light coming from the system - if it should dip suddenly, then regain it's full volume, and this occurs on a regular basis, we can deduct that the big star is being eclipsed by the smaller star, then vice-verse... From this method, we can determine the apparent mass of both stars, and orbital period.

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