Half-Life (scientific term) - could someone explain a few things, please?

Radioactive elements decay until they are no longer radioactive. Unstable elements (ie carbon-14) decay until they are stable. Which means until they are lead. Half-lifes are used to measure the age of something. Carbon dating uses the half life of an unstable type of carbon to measure the age of fossils. As for how, with short half lifestyle they can be easily measured. For long ones, I don't know