Answer:
There are 3 principal radiocarbon dating techniques - gas proportional counting, liquid scintillation counting, and accelerator mass spectrometry (AMS).
Gas proportional counting counts the beta particles emitted by a given sample - a product of radiocarbon decay. Liquid scintillation counting depends on the interaction between the scintillator and the beta particles. AMS dating counts the number of carbon atoms in a sample relative to the carbon 12 and carbon 13 present.
Details found here: http://www.radiocarbon.eu/about-carbon-dating.htm