Scientists can select from many techniques of radiometric dating to determine the age of artifacts as well as the age of Earth itself. Radiocarbon dating is used for dating once-living matter less than 40,000 years old, like wood and charcoal. Uranium dating techniques are used for dating objects from thousands to billions of years old. Both techniques rely on the properties of radioactive isotopes, which are unstable elements that decay into stable ones over time.
In the early decades of the twentieth century, scientists first developed an understanding that certain elements are radioactive and that these unstable isotopes decayed -- or lost particles from their nuclei, thus becoming different elements -- at a constant rate over time. Knowing a radioactive isotope's decay rate, a scientist can say that after a given amount of time, half of the atoms in a radioactive "parent" sample will be transformed into its stable "daughter" product. After another equal amount of time, half of the remaining radioactive atoms will decay. And so on. This is what is meant by "half-life." The half-life of uranium-238, the most abundant isotope of a radioactive element commonly found in the earth's crust, is 4.5 billion years.
Because of its slow rate decay, uranium-238 is commonly used to establish the ages of some of the oldest objects discovered in the earth, including the age of the planet itself. Uranium was incorporated into the earth on its formation. Once fixed in solid rock, its supply of atoms cannot be replenished. Therefore, measuring the amount of the daughter product, lead-206, relative to the parent uranium-238, can help scientists establish the age of a rock sample. Using the uranium's known decay rate they simply calculate back to the time when all of the lead-206 atoms present in the rock were uranium-238 parent atoms. This technique, called radiometric dating, gives them the age of the rock -- and by association, the approximate age of any objects embedded in a sampled rock layer.