They use radio carbon dating of the sediment it was formed in. The sediment itself is formed from a mix of organic and inorganic material, including bacteria, or plant matter. Sometimes you find spores and seeds. The plant matter in the sediment can be accurately dated to when it stopped growing, because the carbon in it will begin to decay predictably at that moment.

So basically it’s the same as if you were studying a plant, but you’re relying on a relatively smaller sample size, and there’s some error because not all the organic matter dies at the same time. But it gives you a range that is pretty close, within a few thousand years.

(ETA: apparently not for things quite this old).