In a word: dendrochronology:
By looking at tree rings, scientists can tell how much carbon dioxide was in the Earth's atmosphere during each year of a tree's life, and since some trees are over 5,000 years old they can look back five millennia.
They can go back even further by looking at long-dead trees and working out, using radio-carbon dating, how long ago the trees died.
And paleoclimatology:
If you want to go back 1.5 million years, the study of ice cores will tell you how much of each atmospheric gas was present in each period's precipitation.
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