How might a geologist study the history of earth?
There are a variety of ways a geologist can study the earth's history. The most obvious, and arguably the most fun for a field geologist, is simply going out into the world and making observations. This can lead to the discovery of new fossils, new rock formations, and otherwise unknown structures which are the foundation of most other geological research.
Specific strategies involve radiometric dating; a geologist can use the knowledge of how radioactive elements decay over time to determine a time frame in which a rock was formed, and may then use that to determine when an event occurred. For example, if a geologist takes two rocks from above and below a point of interest in the earth, such as a fossil, and then dates those rocks, they can detemine a rough timeframe in which the fossil was alive. This is useful in cases where the fossil itself cannot be dated.
A geologist can also use similar strategies with fossils, to determine when certain events took place specifically in relation to life, and with the magnetic orientation of rocks, to determine the alignment of the Earth's magnetic field at different times.
Geologists can also use knowledge of specific rocks and weathering (damage) patterns to determine if specific events occurred. For example, geologists were able to provide evidence for the hypothesis that an asteroid or comet impact killed the dinosaurs, by observing that minerals near the impact site showed evidence of huge amounts of pressure, and that there was a thin layer of the element iridium all over the planet at the same place in the rocks. Iridium is rare on earth, but relatively common in asteroids.