Radioactive isotopes by their nature are unstable and break down (or decay) over time. This can be measured in half-lives. The half-life of a radioactive isotope is how long it takes for half of the nuclei in any given sample to decay. This process goes on at a steady, constant rate for each isotope and scientists are able to use that rate of decay to determine how long the process has been going on (how old the rock is).
Two radiometric methods used for igneous rocks are uranium-lead dating and potassium-argon dating. Both act on the same principal of radioactive decay. Uranium-lead dating uses the decay of two isotopes of uranium, 238U and 235U into isotopes of lead. The closer in agreement the measurements for these separate isotopes are, the more exact and certain the date of the rock. Potassium-argon dating uses the breakdown of an isotope of potassium, 40K, into argon. This can date the rock back to when it first crystallized for an igneous rock or how much time has passed since metamorphosis in a metamorphic rock.