To date, most extrasolar planets have been discovered using the
radial velocity method, where a periodic shift of a star's spectrum betrays a planetary companion. Up and coming is the
transit method, used by the Kepler spacecraft to detect exoplanets passing in front of their parent stars.
Even though it's still behind radial velocity in terms of planets discovered, this method is playing catch-up fast: there are already
thousands of KOIs (Kepler Object of Interest), or exoplanet candidates detected by Kepler that await confirmation using other methods.
From 2013, the
Gaia spacecraft could potentially shift the balance to astrometry as a major planet discovery method. Its mission is to determine star's positions on a scale much more detailed than is possible from Earth, thereby creating a 3-dimensional map of the Galaxy. If a star has a big enough planet, it will wobble and therefore periodically change it's position in the sky.
In this ESA presentation from November 2010 (PPT), it is claimed that Gaia could detect planets down to 10 Earth masses:
Results expected:
~2000 exo-planets (single systems)
~300 multi-planet systems
displacement for 47 UMa = 360 μas
orbits for ~1000 systems
masses down to 10 MEarth to 10 pc