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The passage of time can be charted by the reduction in the number of parent atoms, and the increase in the number of daughter atoms.
Radiometric dating can be compared to an hourglass.
When the glass is turned over, sand runs from the top to the bottom.
Radioactive atoms are like individual grains of sand--radioactive decays are like the falling of grains from the top to the bottom of the glass.
This paper describes in relatively simple terms how a number of the dating techniques work, how accurately the half-lives of the radioactive elements and the rock dates themselves are known, and how dates are checked with one another.