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.

Source: Oldest Rock Speck Zeros In On Earth’s Cooling Date

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.

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The age of a grain is figured by measuring the amounts of the parent uranium isotopes compared to the daughter lead isotopes.