Absolute dating is the process of determining an approximate computed age of something like a fossil. How does that work?
Biostratigraphy - observing which fossils were present in which stratigraphic units, and using minimally-deformed sequences to determine age order - gives us relative ages of fossils.
Absolute ages, however, rely on geochemical chronometers: just like dating the reversals in the Earth's magnetic polarity by establishing how old the oceanic crust that records them, or working out when volcanic eruptions happened. Which chronometer you use depends on exactly what you're working with, but what they all have in common is that they use radiometric dating: the "ticking clock" is radioactive decay, which proceeds according to a radioactive isotope's half-life. Radiocarbon dating can be used for the most recent of these, but the example I'm going to use is uranium-series decay in corals - even though it's a weird one, because unlike most systems it doesn't measure parent-daughter ratios, but rather how closely the system has approached secular equilibrium.
Uranium is soluble in natural waters at conditions found on the Earth's surface; thorium, however, is not; so corals (predominantly calcium carbonate), while growing, continuously incorporate uranium but not thorium. Once they stop growing, this is no longer true - the amount of uranium incorporated in the coral is now fixed. Uranium-234 decays to give thorium-230, which is itself radioactive, with a significantly shorter half-life. At secular equilibrium, the rate of thorium-230 production (from uranium-234 decay) equals the rate of thorium-230 decay, so 230Th reaches steady state. Provided secular equilibrium has not been reached and the concentration of 238U (234U's parent) is also known, it is possible to calculate how long ago the coral stopped incorporating new uranium - became a "closed system". The mathematics of U-series secular equilibria are well understood but somewhat tedious, and are freely available.
Typically this is accomplished through radiometric dating.
While this is a complex field and the article I've provided a link for explains it better than I could here, the short answer is that different elements' isotopes decay to at a known rate, and by measuring the quantities of the isotopes in question (which are chosen depending on the approximately estimated age of the sample), the age of the sample can be calculated.