Radiometric: The radiation emitted by the carbon 14 in a sample is measured. The lower the radiation level, the lower the amount of carbon 14 that remains. Both gas proportional counters and liquid scintillation systems are used for radiometric carbon 14 dating.
Accelerator Mass Spectrometry (AMS): A particle accelerator is used to sort ions according to their mass so they may be counted with special detectors. The advantage of AMS is that only a small sample of a few milligrams is required carbon 14 dating.
The Shroud of Turin was dated using AMS. The procedure was relatively new in
1988, but that is not considered a problem.
Both methods produce accurate results. The radiometric method is simpler and less costly but requires larger samples. AMS only requires very small samples but it is costly because of the complex equipment used.
Both methods require that the sample be destroyed to convert the carbon into a usable form for measurement.
Carbon 14 testing is only accurate for material that is less than 50,000 years old.