How do we know that there were over 420 days a year, 600 million years ago? By counting.
You only need walk in the woods from time to time to know that trees like the summer more than the winter. They grow faster when it is warmer and therefore their age can be determined by counting growth rings. But some creatures express other periodicities as well. Corals and other creatures that form solid shells grow in the hours of daylight, when they build up rocky material. At night they stop. Between one day's growth and the next, you get a slight band which can be observed with a microscope. There are also monthly growth bands – which can be harder to spot – caused by the rise and fell of the tides giving the coral more or less nutrition. And because the summer days are longer and hotter than days in winter, there are annual rings caused by the fact that the daily rings formed in summer are fatter than the ones laid down in winter. Look closely enough and you can count over 400 of the daily variety for each annual ring in a Cambrian shell from 600 million years ago.
Left to itself, nature provides all kinds of clues about its age. Take varves, for example. These lake deposits mainly encountered in Sweden tell us about the chronology of the past in a unique way. When the snow melts, spring floods wash large amounts of mud into the lakes, where it is laid down in dark layers of coarse sediment. Later in the year, fine, light sediment can settle because the water has become calmer. So a varve is a pair of light and dark sediment layers. Its thickness reflects the weather in a specific year so that – like tree rings – you can use them to build up lengthy climate records. Even better, the streams that fill up the lakes carry pollen and other plant debris with them so that the varve material also contains a record of the local ecology at the time.