Astronomers study the light of spectral lines of stars to see if they are moving back and forth, this indicates whether they have a planet orbiting them. As the planet orbits the star, it pulls on its gravitational field causing the star to “wobble”, the star will at times be moving towards earth and at other times be moving away and this results in the Doppler effect.  The transit method is based on the observation of a star’s brightness. As a planet orbits the star, it passes in front of the star causing there to be a drop in brightness.
By observing the repeated occurrence of the drop in brightness astronomers can determine if the drop is really from a planet.  The direct method of finding an extrasolar planet is much more difficult than using the indirect method, as planets further away are usually dimmer compared to their parent stars. However new techniques are being created such as the use of interferometry where the light of various telescopes are combined to “overcome the diffraction-limit of an individual telescope.