In addition to various pre-treatments, the sample must be burned and converted to a form suitable for the counter. The sample must be destroyed in order to measure its C-14 content.

The first measurements of radiocarbon were made in screen-walled Geiger counters with the sample prepared for measurement in a solid form. These so-called "solid-carbon" dates were soon found to yield ages somewhat younger than expected, and there were many other technical problems associated with sample preparation and the operation of the counters. Gas proportional counters soon replaced the solid-carbon method in all laboratories, with the samples being converted to gases such as carbon dioxide, carbon disulfide, methane, or acetylene. Many laboratories now use liquid scintillation counters with the samples being converted to benzene. All of these counter types measure the C-14 content by monitering the rate of decay per unit time.

A more recent innovation is the direct counting of C-14 atoms by accelerator mass spectrometers (AMS). The sample is converted to graphite and mounted in an ion source from which it is sputtered and accelerated to targets tuned to different atomic weights. The proportion of hits on the different targets reveals the amount of C-14 in the sample.

Further reading:

Radiocarbon home page
http://www.radiocarbon.org