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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.
Archaeologists had used Relative Dating methods to calculate their reigns.
Though their initial calculations were slightly incorrect thanks to the contaminants of extensive nuclear testing of the age, scientists soon discovered the error and developed methods that were more accurate, including a date of calibration to 1950.
This new method was based on gas and liquid scintillation counting and these methods are still used today, having been demonstrated as more accurate than Libby's original method (3).
So in order to date most older fossils, scientists look for layers of igneous rock or volcanic ash above and below the fossil.
Scientists date igneous rock using elements that are slow to decay, such as uranium and potassium.