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how can we determine the age of rocks and other materials?
One common method is radiometric dating. It relies on the decay of radioactive isotopes. For example, carbon - 14 dating for relatively young organic materials (up to about 50,000 years old). Uranium - lead dating is used for older rocks (billions of years old). Another way is stratigraphy. By looking at the layers of rocks (strata), in general, lower layers are older (law of superposition). Fossils within the rocks can also help as certain fossils are characteristic of specific time periods (biostratigraphy).
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Radiometric dating (e.g., carbon - 14, uranium - lead) and stratigraphy (including biostratigraphy using fossils) are ways to determine the age of rocks and materials.