As this is a red dwarf star, it is smaller, dimmer and therefore cooler than our sun. As a result, the Gliese 581 habitable zone is a lot more compact than our sun's. Gliese 581d - a "super-Earth" with a mass seven times that of our planet - skirts the outermost edge of the Gliese 581 habitable zone and has an orbital period of only 67 days. Gleise 581g on the other hand is thought to be around three-times the mass of Earth and orbits right in the middle of the star's habitable zone. Its orbital period has been clocked at 37 days. (It is worth noting, however, the very existence of Gliese 581g has been called into question.)
Naturally, the mere hint of these "habitable" worlds in Gliese 581 has caused some excitement - they could host the perfect conditions for life (as we know it) to thrive. If there's life, then perhaps it evolved to support intelligence; if there's intelligence, then perhaps it has gone through a similar "radio transmitting" phase as us.
The Search for Extraterrestrial Intelligence (SETI) has a few tricks up its sleeve to look for these hypothetical intelligent radio-transmitting aliens. Firstly, space is vast, and there are a lot of stars out there, so (until recently) the most effective method for searching for a SETI signal has been to "cast the net as wide as possible." Using radio telescopes, surveys have scanned the sky. If an interesting signal is detected in the survey, astronomers can hone in on it for further study.