The best resource in book form I have found that discusses how the age of the Earth is known is The Age of the Earth by Brent Dalrymple. It is a bit of a dry read but packed with info. There are also good summaries at Talk Origins the first being by Dalrymple himself.
It sounds like they used the Uranium-Lead concordia method (also described here), which takes advantage of the fact that there are two different ways Uranium decays into lead. One from U-238 to Pb-206 and another from U-235 to Pb-207. It is a particularly useful test because zircon doesn’t incorporate lead into its crystal at the time it forms.
The oldest remaining grain of early Earth’s original solid rock crust has now been confirmed to be a 4.374-billion-year-old old zircon crystal from Jack Hills, Australia.
That age should settle a scientific debate over the accuracy of that mineral’s internal clock, and cuts the time from when Earth was hit by a Mars-sized body (which led to the formation of the Moon) and the cooling and creation of Earth’s first solid crust from 600 million years to 100 million years.
The age of a grain is figured by measuring the amounts of the parent uranium isotopes compared to the daughter lead isotopes.