All radioactive isotopes have a characteristic half-life (the amount of time that it takes for one half of the original number of atoms of that isotope to decay).By measuring the parent isotope (radioactive) and the daughter isotope (radiogenic) in a system (for example, a rock), we can tell how long the system has been closed (in our example, when the rock formed).
For example, a problem I have worked on involving the eruption of a volcano at what is now Naples, Italy, occurred 38500 years ago with a plus or minus of 300 years.
So, when the materials are appropriate and one carefully avoids contamination and re setting radiometric clocks can be VERY ACCURATE.
The process of radiogenic dating is usually done using some sort of mass spectrometer.
A mass spectrometer is an instrument that separates atoms based on their mass.
It is commonly used in earth science to determine the age of rock formations or features or to figure out how fast geologic processes take place (for example, how fast marine terraces on Santa Cruz island are being uplifted).
Radiometric dating relies on the principle of radioactive decay.
This is an enormous branch of geochemistry called Geochronology.
It is an accurate way to date specific geologic events.
We have dated meteorites using Rb-Sr, Sm-Nd, Pb-Pb, Re-Os, and Lu-Hf isotope systems and have obtained very similar ages.