Well, it can't be explained as if a person had little scientific education, unfortunately.
All that I'll say is this:
1. All atomic structures absorb wavelengths of the light spectrum (visible AND others) differently.
2. When you pass full spectrum light through a gaseous amount of a molecule (DMS or whatever), the atoms in the molecular structure absorb certain wavelengths as does the structural arrangement; so molecules also have specific light wavelength absorption fingerprints. This is how all molecule-identifying spectroscopy works today. Our commonly used alternative testing (Mass Spec) requires an in-hand sample, so we are stuck with light spectroscopy.
3. Suns create nearly full spectrum light. (even after their light escapes through their own atmospheres, it is fairly "full". Different stars are classified as to what wavelengths their atmospheres absorb. If you know the star type, you know what its light spectrum [full minus what it absorbs itself] should look like. In this case that almost doesn't matter as we are comparing sort of a status quo vs interference state condition.
4. If something else passes between us and the star, and its surrounding gases absorb the star light in its path to us, that something's molecules absorb their characteristic wavelengths just as they would do to a light source we shown on them in the lab. That star light would emerge through those clouds minus the absorbed wavelengths, and keep on to us.
5. When we see the light from the Sun of that system, it will be minus the wavelengths it itself absorbed, and the wavelengths that the intervening planet (or even a gaseous cloud) absorbed. When the planet moves out of the way, the spectrum changes and the otherwise absorbed light lines return. So we know which molecules were in the atmosphere or intervening cloud.
6. All that has been known, and sort of understood (as much as anything really fundamentally microcosmic can be understood.) The problem therefore is technological, not scientific. All such discoveries have waited until we could manage the light-sensitive-gathering ability to collect enough light to measure things at all. We're still WAY short of we really need in light-gathering tech.
