In a way this field, called geochronology, is some of the purest detective work earth scientists do.
There are two basic approaches: relative age dating, and absolute age dating.
One way that helps scientists place fossils into the correct era on the Geologic Time Scale is by using radiometric dating.
Also called absolute dating, scientists use the decay of radioactive elements within the fossils or the rocks around the fossils to determine the age of the organism that was preserved.
To determine the relative age of different rocks, geologists start with the assumption that unless something has happened, in a sequence of sedimentary rock layers, the newer rock layers will be on top of older ones. This rule is common sense, but it serves as a powerful reference point.
We can then use radioactive age dating in order to date the ages of the surfaces (when the rocks first formed, i.e. We also have meteorites from asteroids and can date them, too.
These are the surfaces that we can get absolute ages for.
For the others, one can only use relative age dating (such as counting craters) in order to estimate the age of the surface and the history of the surface.
When Rutherford announced his findings it soon became clear that Earth is millions of years old.
These scientists and many more after them discovered that atoms of uranium, radium and several other radioactive materials are unstable and disintegrate spontaneously and consistently forming atoms of different elements and emitting radiation, a form of energy in the process.