You can get some idea of how this is done from the link you provided. It differs depending on the dating method, like for Carbon-14 the amount of it in the envi

You can get some idea of how this is done from the link you provided. It differs depending on the dating method, like for Carbon-14 the amount of it in the environment is pretty much constant (Carbon-14 is generated in the upper atmosphere). So you can date an organism by when it stopped taking in new carbon, i.e. when it died. For other, longer-lived isotopes, keep in mind you are not just measuring the amount of radioactive material left, but are also measuring the amount of the daughter product mixed in some proportion with it. And the proportions in the material being dated might not be the same as what they are in the surrounding environment (in fact, can not be, if the dating method is going to work). As a simple example, you could date rocks with uranium and lead, since you would expect there to be more lead in old rocks because some of the uranium decayed to lead. However, if that rock melted and mixed with younger rocks, the proportion of lead and uranium would cease to be of any interest.