[welterde]

So first of these are not images of stars, but spectra. From these spectra you can extract quite a number of observables, such as radial velocity (how fast it is coming towards/moving away from us) in this case.

Since planets orbiting stars are not massless, both the star and the planets orbit a common center of mass, causing the star to periodically move toward/away from us (much more complicated of course with multiple planets, plane of the planets, oscillations in the star itself, etc.) - which we can measure.

To find exoplanets using this methods you need spectographs, which are very stable in the long-term (especially if you are interested in lower mass planets) and can measure radial velocities in the range of 1 m/s, such as HARPS [1].

[1] http://www.eso.org/sci/facilities/lasilla/instruments/harps/...