Uses of radioactive carbon dating
By measuring the ratio of Carbon-14 in a sample and comparing it to the amount in a recently deceased sample its date can be determined.
If you ever wondered why nuclear tests are now performed underground, this is why.
Most radiocarbon dating today is done using an accelerator mass spectrometer, an instrument that directly counts the numbers of carbon-14 and carbon-12 in a sample.
A detailed description of radiocarbon dating is available at the Wikipedia radiocarbon dating web page.
Over time there is a gradual decrease in the amount of Carbon-14 and the ratio of Carbon-14 atoms to other Carbon atoms declines. Therefore half of the Carbon-14 has decayed after 5730 years.
Half of the remaining Carbon-14 then decays over the next 5730 years leaving one fourth of the original amount.