One of the great problems in the search for exoplanets is detecting the darn things. Most are simply too small and too far away to be observed directly. Our Earth-based telescopes can't resolve a faraway planet as a dot separate from its host star. Luckily, astronomers have other means at their disposal, and they all call for sophisticated telescopes armed with photometers (a device that measures light), spectrographs and infrared cameras.
The first method, known as the wobble method, looks for changes in a star's relative velocity caused by the gravitational tug of a nearby planet. These tugs cause the star to surge toward Earth and then away, creating periodic variations that we can detect by analyzing the spectrum of light from the star. As it surges toward Earth, its light waves are compressed, shortening the wavelength and shifting the color to the blue side of the spectrum. As it surges away from Earth, its light waves spread out, increasing the wavelength and shifting the color to the red side of the spectrum. Larger planets intensify the wobble of their parent stars, which is why this technique has been so efficient at finding gas giants several times larger than Earth.
What's one thing that all planets can do well? Block light. If a planet's orbit crosses between its parent star and Earth, it will block some of the light and cause the star to dim. Astronomers call this a transit, and the related planet-hunting technique the transit method. Telescopes equipped with sensitive photometers can easily discern large planets, but they can also catch even the slight dimming caused by an Earth-sized object.
Finally, some astronomers have been turning to a technique known as microlensing. Microlensing occurs when one star passes precisely in front of another star. When this happens, the gravity of the foreground star acts like a magnifying lens and amplifies the brightness of the background star. If a planet orbits the foreground star, its additional gravity intensifies the amplification effect. This handily reveals the planet, which would otherwise be invisible to other detection techniques.