There are several methods currently used to detect exoplanets. Some of these are more effective than others at finding exoplanets (see Figure 1) of a particular type (such as the 'hot Jupiters' or 'Earth-like' object).
Astrometry: detecting tiny changes in a star's position caused by the presence of an exoplanet or exoplanets.
Direct Imaging: spotting the faint glow of a planet far from its parent star by blocking the star's light.
Gravitational Microlensing: using the chance alignment and lensing effect of two stars with the nearer one to us having an exoplanet.
Pulsar Timing: detecting the time varying arrival of radio waves from energetic, highly magnetic neutron stars.
Radial Velocity: using spectroscopy to detect the characteristic blue- and red-shift of a star as its orbit is perturbed by an exoplanet.
Transit: detecting an exoplanet as it crosses the face of its parent star causing the light we detect to dim.