http://en.wikipedia.org/wiki/Radiometric_dating
http://en.wikipedia.org/wiki/Radiocarbon_dating
We know the half-lives because we can put the materials in the lab and determine how much of the material decays over a given period of time, and then we simply extrapolate that out to thousands of years. There are certain materials that have half-lives of days, so we know how radioactive materials behave and what they do.
Mind you, radiometric/radiocarbon dating is only accurate out to a point, when we start to use fossil layers and other materials found near the dated material for dating purposes.