[roelschroeven]

I would guess spectral analysis of the light coming from the planet's star. Look at the spectrum when the planet is behind the start, look at the spectrum when the planet is in front of the star (in which case part of the light passes through the planet's atmosphere). The difference between the two indicates which frequencies are absorbed by the planet's atmosphere, from which its composition can be determined. Don't take my word for it though, I'm not an astrophysicist.

In any case it boggles my mind that we can do things like that for planets thousands of light-years away from us.