Obviously, if the substance you are measuring is contaminated, then all you know is the age since contamination, or worse, you don't know anything, because the contamination might be in the opposite direction - suppose, for example, you're looking at radio carbon (carbon 14, which is produced in the atmosphere by cosmic rays, and which decays into nitrogen).
Since you are exposed to the atmosphere and contain carbon, if you get oils from your skin onto an archeological artifact, then attempting to date it using radio carbon will fail because you are measuring the age of the oils on your skin, not the age of the artifact.
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.
They can then look at a single mineral, and using an instrument called a mass spectrometer, they can measure the amount of parent and the amount of daughter in that mineral.
Hope that helps, and please ask if you'd like more details! I think that I will start by answering the second part of your question, just because I think that will make the answer to the first question clearer.
We know it is accurate because radiometric dating is based on the radioactive decay of unstable isotopes.
The decay constants for most of these systems have been confirmed in other ways, adding strength to our argument for the age of the earth., so there is one zirconium (Zi) for one silicon (Si) for four oxygen (O).
One of the elements that can stand in chemically for zircon is uranium.
All radioactive isotopes have a characteristic half-life (the amount of time that it takes for one half of the original number of atoms of that isotope to decay).
By measuring the parent isotope (radioactive) and the daughter isotope (radiogenic) in a system (for example, a rock), we can tell how long the system has been closed (in our example, when the rock formed).
For example, a problem I have worked on involving the eruption of a volcano at what is now Naples, Italy, occurred 38500 years ago with a plus or minus of 300 years.