To determine how much carbon-14 there was initially, one can use the amount of carbon-12 present in the organic material currently (carbon-12 is stable) and use a ratio of about 1 carbon-14 for every trillion carbon-12’s to calculate.

There are neat systems out there for determining ages of sites, including older sites than 60,000 years.  Potassium-argon dating, for instance, measures the radiation in a radioactive form of potassium within volcanic ash.