What type of search technique has discovered the second largest number of exoplanets?

looking for tiny variations in the suns radial velocity, caused by the gravitational pull of one or more planets orbiting the star

A number of sophisticated methods for identifying planets have been developed. These techniques are used on a wide range of ground-based and space-based instruments, and are being combined to provide more detailed and accurate data. 
An exoplanet (or extrasolar planet) is a planet orbiting a star different from the Sun (the "exo" prefix means "outside" in Greek). Up until now, one has found mainly gas giant planets, which are easier to detect than telluric planets. However, due to the increasing sensitivity of the detection methods, one already begins to observe the first planets of sizes comparable to the Earth.