Planet Hunting is the action of looking for planets in solar systems, other than our own. While stars such as our sun emit light, the planets which orbit it, can only reflect that starlight from their surface.
There are nine planets which orbit our sun, and up until 1991 we had no evidence of planets orbiting other stars, in other solar systems. The first two extrasolar planets were found orbiting a pulsar in the constellation Virgo, they were discovered by astronomer Alex Wolszczan.
While we cannot see distant planets, because their parent star outshines them, we can detect the small effect they have on the star they orbit. As a planet orbits a star, it creates a slight wiggle in the star's position; this is caused by the planet's gravitational force, which pulls the parent star towards itself, as it revolves the star.
Another effect we can measure, is the star's light density. As a planet moves between the star and our view path, an eclipse occurs; at that time, the light density of the parent star drops by a few percents -- allowing us to visualize the orbiting planet.
The third method of detecting distant planets known as Doppler Spectroscopy. By analayzing the spectrum of the light that comes from an object we can establish when the object moves. Once the wavelength of that light changes, we can tell whether the object got closer to our location or further from it. This tells us that the star moved, probably because it was pulled further from Earth by an orbiting planet which is located directly behind it (from our point of view on Earth).
For the time being, we have detected hundreds of distant planets, and new discoveries take place constantly. But because planets vary in their mass, composition and distance from the star -- small planets have yet been discovered. This occurs because only large planets have a detectible effect on their parent stars. This unfortunately means that we cannot detect distant Earth-like planets; but do not worry, as NASA is already working on a solution.
Terrestrial Planet Finder is NASA's solution for detecting distant Earth-like planets. The Terrestrial Planet Finder is constructed of four telescopes, spread on at least a kilometer (0.6 miles) baseline. The wide baseline will allow the telescopes to cancel out the stars glare, a technique known as nulling interferometry. The next step will be examining the planet's infrared spectrum, detecting whether its atmosphere contains substances which could indicate an Earth-like environment.