How do scientists analyze the TRAPPIST system?

A team led by Michaël Gillon at the University of Liège in Belgium detected the planets using transit photometry with the Transiting Planets and Planetesimals Small Telescope (TRAPPIST) at the La Silla Observatory in Chile and the Observatoire de l'Oukaïmeden in Morocco.

Explanation:

This is just how the TRAPPIST system was discovered.

Here's the link about the information you need:

https://www.nasa.gov/press-release/nasa-telescope-reveals-largest-batch-of-earth-size-habitable-zone-planets-around