Refer to the links for a page describing the process.
The universe is full of naturally occurring radioactive elements.
The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.
The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained.
Scientists date igneous rock using elements that are slow to decay, such as uranium and potassium.
By dating these surrounding layers, they can figure out the youngest and oldest that the fossil might be; this is known as "bracketing" the age of the sedimentary layer in which the fossils occur.
Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.
So in order to date most older fossils, scientists look for layers of igneous rock or volcanic ash above and below the fossil.
By contrast, methane created from petroleum showed no radiocarbon activity because of its age.
The results were summarized in a paper in Science in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin.
For consistency with these early papers, and to avoid the risk of a double correction for the incorrect half-life, radiocarbon ages are still calculated using the incorrect half-life value.
A correction for the half-life is incorporated into calibration curves, so even though radiocarbon ages are calculated using a half-life value that is known to be incorrect, the final reported calibrated date, in calendar years, is accurate.