I have begun to read more about how to determine the age of archeological findings. I think I understand the basic premise of radiometric dating methods but I am not sure if I got some of the details right. Maybe one of you can help me understand it better?

So, the idea is that radioactive isotopes decay over time into stable isotopes. We use the half-life of an isotope as the decay rate. By measuring the amount of stable isotopes (with mass spectrometry) in a rock or mineral one can deduce how much time must have passed for this amount to be present. Because different isotopes have different half-lifes one can cross-check the first estimate by looking at the amount of other stable isotopes that are the decay product of radioactive isotopes with a shorter half-life. This method only works when the stable isotopes can only be the result of a decay process and can not be present without said process. In this way, it is not necessary to know how much of the radioactive isotopes were present at the time when the rock was formed because we can estimate the age by "calculating backwards" from the amounts of the stable isotopes which are a direct result of the decay process that took place over hundreds of thousands of years.

Please understand that I am not a chemist or geologist. This is what I pieced together from information I found on the internet. Is this correct? Did I miss something? Do you have suggestions for good and newcomer friendly introductions to this topic?