Mental_Floss has compiled a lit of ten interesting methods scientists use to date things, from extracting DNA from the pages of medieval manuscripts to studying what the climate must have been like in the past through pollen.
Left and right, archaeologists are radiocarbon dating objects: fossils, documents, shrouds of Turin. They do it by comparing the ratio of an unstable isotope, carbon-14, to the normal, stable carbon-12. All living things have about the same level of carbon-14, but when they die it begins to decay at uniform rate—the half-life is about 5,700 years, and you can use this knowledge to date objects back about 60,000 years.
However, radiocarbon dating is hardly the only method that creative archaeologists and paleontologists have at their disposal for estimating ages and sorting out the past. Some are plainly obvious, like the clockwork rings of many old trees. But there are plenty of strange and expected ways to learn about the past form the clues it left behind.