For an example of how geologists use radiometric dating, read on: A geologist can pick up a rock from a mountainside somewhere, and bring it back to the lab, and separate out the individual minerals that compose the rock.
We have also obtained a very similar age by measuring Pb isotopes in materials from earth.
I should mention that the decay constants (basically a value that indicates how fast a certain radioactive isotope will decay) for some of these isotope systems were calculated by assuming that the age of the earth is 4.56 billion years, meaning that we will also calculate an age of 4.56 billion years if we use that decay constant.
The process of radiogenic dating is usually done using some sort of mass spectrometer.
A mass spectrometer is an instrument that separates atoms based on their mass.
The man's body was recovered and pieces of tissue were studied for their C content by accelerator mass spectroscopy.