If you have a bit of time, check out this relaxed presentation with Tony Darnell as he discusses with Jessie Christiansen, David Ciardi, and Courtney Dressing (Caltech) the techniques used to combine clever ideas and several telescopes to find these planets.
(Afternoon astronomy coffee hangout)
An extraordinary discovery of numerous exoplanets was made by combining NASA's K2 mission data with follow-up observations by ground-based telescopes including the W. M. Keck Observatory and Gemini on Mauna Kea, and a twin Gemini telescope in Chile. Of the numerous exoplanet candidates found, more than 100 are confirmed planets. One system has four planets possibly similar to Earth.
The researchers are using the new method for observing with the planet finding Kepler telescope, a mission called “K2”. In the new observing scheme, the satellite is moved to different fields making innovative studies possible. By using multiple observatories world wide, the researchers could verify and diagnose the exo-planets..
Master of Golden Age science fiction Edmond Hamilton described the idea of an automated habitable planet-finding telescope in his 1936 short story Cosmic Quest:
I was near enough it now to set my automatic astronomical instruments to searching it for a habitable planet.
These instruments were the wonderful ones our astronomers had perfected. With super-telescopic eyes each one scanned a part of the star field before them. And each mechanical eye, when it found planetary systems in its field, automatically shifted upon them a higher powered telespectroscope which recorded on permanent film the size, mean temperature and atmospheric conditions of these worlds.
(Read more about Hamilton's search for habitable planets)