The Science Geek blog has a detailed account of the discovery of seven Earth-sized planets orbiting a small cool star known as Trappist One. It begins:
Trappist-1 and its planets were discovered by a team from the University of Liege in Belgium, using a telescope in Chile called TRAPPIST – the TRAnsiting Planets and PlanetesImals Small Telescope. The team discovered the planets through their study of the way the light from Trappist-1 varies over time. Planets other than those in our solar system are known as exoplanets, and all exoplanets are much too faint to be seen directly from Earth. However, as shown in the diagram below, as a exoplanet passes in front of a star the brightness of the star dims because some of its light is blocked from reaching the Earth. …
The blog has lots of details, charts, graphs and diagrams – and even a picture. There’s much here for the astronomically-minded.