The theory behind radiometric dating is actually quite simple. Every Atom of a given element has the same number of protons, but there are varieties in the number if neutrons. These varieties are called isotopes. Some of these isotopes decay (parent isotope) into other isotopes of other elements (daughter isotope). The time is takes for half of a sample of a given isotope to decay is called its half life. The half life of a given isotope can be as small a fractions of a second to billions of years. Some as far as we know are stable and do not decay.
Measurements of the half lives show that in general they are constant though there have been some reports of small variations. It is these half lives that form the theoretical bases of radiometric dating. The basic idea is that if you have x amount of the parent isotope and y amount of the daughter isotope that given a constant half life you can calculate how much time parent isotope would have to decay to produce the measured amount of the daughter isotope.
Next the assumptions of Radiometric dating