Star and planet orbiting their common centre of mass
This animation shows how the presence of a planet orbiting a star is reflected in the star's motion. In fact, both the star and the planet orbit the common centre of mass. Since most of the mass in the star-planet system is concentrated in the star, the centre of mass is located within the star.
The motion of the star, wobbling around the centre of mass, can be detected either via astrometry, by measuring how the star's position varies over time, or via the radial velocity technique, by measuring periodic shifts of absorption lines in the spectrum of the star.
Scientists expect that ESA's Gaia mission will detect some tens of thousands of exoplanets out to 500 parsec (around 1600 light-years) from the Sun with the astrometric technique.
It is not expected that Gaia will detect exoplanets using the radial velocity technique; however, the mission will provide useful measurements to identify false detections because the accuracy will be sufficient to clarify that some candidates are double stars rather than stars with an orbiting planet.