How can the absolute age of earth layers be determined?
Almost entirely by radiometric age dating of certain minerals.
Scientists discovered that certain elements decay into other elements at a very constant and predictable rate - called, the "half-life". For example, Uranium decays to lead, rubidium decays to strontium, potassium to argon and so on.
So, in the pic included if you start with a mineral that has say 25 of the yellow uranium atoms in it, after 1 billion years, 1/2 have decayed to thorium, after another billion years, another 1/2 have decayed to thorium, and so on. By knowing this decay half-life, the age of the sample, and hence the rocks the sample came from, can be determined.