" Every matter must be established by the testimony of two or three witnesses. " - 2 Corinthians 13:1.
There are two obvious possibilities. Each layer could be one year; or each layer could be one snowstorm. So, when the ice layers were first discovered, it wasn't clear what they meant. Quite a few scientists had a shot at the problem.
One idea was to measure an isotope ratio. Specifically, the ratio of Oxygen-16 to Oxygen-18. These occur naturally in ocean water, and form water molecules of slightly different weight. The heavier water molecules don't evaporate quite as easily. So, it's not surprising that the heavy-to-light ratio is a bit larger in the ocean than in Arctic and Antarctic snow. And, the ratio in the snow changes, with more "heavy" molecules in the summer than in the winter.
A particularly warm year, or cold year, would affect this. But in any case, as you measure deeper and deeper in the icecap, you would expect the ratio to go up and down and up and down. In short, it should be cyclic, until you get so deep that everything smears together. And each cycle is one year.
So, now we have a way to answer the basic question: how many layers per year? And the answer turns out to be: one. To be more precise, it is thought that in the last 50,000 years, the deviation from 1:1 is much less than 1%. That is, the best possible count to layer 50,000 would mis-date by much less than 500 years.
The oxygen ratio isn't the only method used to draw that conclusion. The deuterium ratio follows the same pattern. And then there's the ratio of Beryllium 10 to Beryllium 9. This is a little different, because Be10 comes from the upper atmosphere, not from the ocean. And, one cycle of this ratio represents a Solar sunspot cycle, which is to say, 11 years.