How can we extract atmospheric molecules from exoplanet transmission spectra?

[Jack.R]

I'm an amateur astronomer who has been following exoplanet discoveries for years, and with the latest data releases from missions like TESS and JWST, I'm trying to wrap my head around the methods used to characterize atmospheric composition from transmission spectra. I understand the basic principle of light passing through an exoplanet's atmosphere, but the specifics of spectral line analysis and dealing with noise from the host star are confusing. For those more knowledgeable in astrophysics, can you explain the key steps and challenges in going from a raw light curve to confidently identifying molecules like water or methane in a distant world's atmosphere?