Among the methods developed by astronomers, two of them have provided most of the significant results up to now.
With the first method, we measure the small movements of the star produced by the presence of a planet.
Indeed, in the same way as the head of a hammer thrower oscillates when his hammer makes a circle around him, it is possible to measure on stars a small wavering, which is synchronous with the revolution of the planet around the star.
With this method, M. Mayor and D. Queloz detected the first extrasolar planet around the 51 Pegasi star. The vast majority of the 245 exoplanets known today (July 2007) have been discovered with this method. This technique allows us to deduce the radius of the planet's orbit, and to get a good idea of its mass.
With the second technique, we try to detect the passage of a planet in front of the host star (the transit), measuring the small variation of brightness due to the partial masking of the star. But to observe such events, we (on Earth) have to be in a good position : first, the Earth, the star and the exoplanet must be aligned, which is quite unusual; and second, we must observe the transit at the right moment. With this technique, we can derive the size of the planet. The transit method will be used for example by the CoRoT satellite.