Final answer:
The most successful methods for finding exoplanets are Doppler shifts and transits, with transits being particularly effective when used by space observatories like Kepler.
Step-by-step explanation:
The techniques that have been the most successful at finding exoplanets are the Doppler shifts (radial velocity) and transits. The Doppler method utilizes high-resolution stellar spectroscopy to detect the wobbles in a star's movement, caused by the gravitational pull of an orbiting planet, which changes its radial velocity in a detectable way, allowing us to find planets that are both massive and close to their stars.
On the other hand, the transit method involves monitoring the light from a star for periodic dips in brightness as a planet passes in front of it, which can be observed from space via the Kepler space observatory with high precision. Both methods have biases but have been very successful in identifying numerous exoplanets, particularly when they orbit close to their star and are large in size.