How to Analyse Past Atmospheres
I came across THIS ARTICLE and found it very interesting. It describes methods used to extract and analyse gases trapped in rocks and minerals. The gases are in various salts, quartz and crystallized magmas.
The technique used sounds simple - crush the rock and collect the gas. But it has to be done in a vacuum-sealed press and send the released gas to a mass spectrometer for analysis. The gas does not all come out at once but in pulses as different parts of the sample fail. Repeat and repeat until you have enough gas. The crushers are very small - 10 grams of rock is considered "an insane quantity"!
Crush Archaean rocks and with care you can get a sample of Archaean air. Its age can be proved by radiometric dating of the included noble gas isotopes. There have been some surprises - higher oxygen levels appearing earlier than expected.
But read the article to get an introduction to this fascinating subject.