We're able to identify non-stellar companions by the telltale signatures they impose on the central star as it moves through space. Basically, we're seeing perturbations or wobbling of the star caused by the gravitational nudges of a companion. The wobble can be detected by very sensitive instruments which measure variations in the velocity of an object. By tracing the wobbling patterns, astronomers can determine if one or more companions are responsible, and estimate how far from the star the planets must be to produce the observed perturbations. The more exaggerated the wobbling, the more massive the planet.
Astronomers are able to gage the mass of the planets if they have an idea of how far away they are.
If there's more than one companion, they'll be additional layers of perturbations evident on the tracings. We don't always know, however, if the companion we're seeing is really a planet or a brown dwarf star, the burnt out husk of a failed star. The spectrum of the companion would help let us know whether or not we're detecting a brown dwarf or a planet, but the distances are too great and the objects too small to collect enough light for spectral analysis. About eight of the 15 orbit uncomfortably close to their sun - they take less than three weeks to make a complete revolution. The nearest star to us, which is a candidate for having a solar system, is a star named Gliese 876.