How do astronomers determine that they've discovered "single" large extrasolar planets and not "multiple" lesser planets?

We detect extrasolar planets not by observing the planets directly (they're too small and lost in the glare of the parent star), but by observing the motion of the parent star and asking whether it seems to be moving due to the gravity of an unseen planet or planets. As a planet revolves around a star, the star too revolves a bit around their common center of mass. A large planet will cause a sinusoidal shift at a single frequency (the time of that planet's year) in the star's apparent motion towards or away from us. Two planets will have two different length years, and cause wobbles in the star's motion of two different frequencies. That's how we know when we're looking only at a single planet.

Some stars have indeed been seen to exhibit multiple large planets. I should also note here that using this method we are only able to detect planets the size of Jupiter or larger. Small planets like Earth are too small for their gravity to have a measurable effect at the moment. At some point in the future refinements in this technique or other techniues may allow us to see Earth-like planets.