Common isotopes for radiometric dating
After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide, or decay product.
To measure the passage of long periods of time, scientists take advantage of a regularity in certain unstable atoms.
In radioactive atoms the nucleus will spontaneously change into another type of nucleus.
When looking at a large number of atoms, you see that a certain fraction of them will change or dating system because you can determine accurate ages from the number of remaining radioactive atoms in a rock sample.
Or you can tell that certain parts of the Moon's surface are older than other parts by counting the number of craters per unit area.
The old surface will have many craters per area because it has been exposed to space for a long time. If you assume that the impact rate has been constant for the past several billion years, then the number of craters will be proportional to how long the surface is exposed.