Past atmospheric C-14/C ratios are assumed to equal the present ratio, so dead plant or animal matter is assumed to have had the present ratio at its death. Measuring the C-14 left in the dead plant or animal matter gives an estimate of the time it has been dead. If there is 1/2 the present ratio left, it is assumed to have been dead one half-life (about 5730 years); if there is 1/4 the present ratio left, its C-14 date is two half-lives (about 11460 years); etc. The situation is really more complicated than this -- the atmospheric C-14/C ratio has varied in the past and so some sort of calibration curve is necessary.
2010 Arthur V. Chadwick, Ph.D.