Researchers used the European Southern Observatory in La Silla, Chile and an instrument known as HARPS - the High Accuracy Radial velocity Planet Searcher - a spectrograph that can detect extremely minute "wobbles" in stars caused by the gravitational attraction of orbiting planets (just one of several different techniques currently used to search for exoplanets).
The wobble of this star was complex and some advanced computer processing was required to determine that the motion could be explained by 5 Neptune-sized planets orbiting closer to HD-10180 than Mars orbits to our Sun. (Just to be clear, while we have directly imaged some exoplanets, others, like these, are indirectly inferred from their effects on the parent star). There's also the possibility of another Saturn-sized planet close in to the star as well as a planet 1.4 times the size of the Earth (would be the least massive explanet found if confirmed) orbiting the star every 1.18 Earth days!
In the past decade, sophisticated astronomical instruments have allowed us to detect hundreds of exoplanets through a variety of techniques. So far, these exoplanets have been large gas-giant types (like our Jupiter, Saturn, Uranus, and Neptune) since it's easier to detect large exoplanets. Small rocky planets like our Mercury, Venus, Earth, and Mars are what most astronomers really want to get at because that's where we're most likely to find life. One of the things we've seen, however, is that most of these other solar systems are really strange places compared to our own. It may be that our solar system, with its nice arrangement of 4 terrestrial planets and 4 gas-giant planets, with the Earth in a nice zone for liquid water, may be an aberration. But, who knows, the universe is a big place!
Artist's conception of an extrasolar planet from Astronomy Picture of the Day