Maybe they didn't try to divide the year up into fixed pieces like we do. Maybe they related everything to the solstices and equinoxes and then to the lunar cycles and then to days. In other words you might plant a particular crop on the third day after the second full moon following the spring equinox. So variations in the length of the year would be essentially irrelevant.
The relationship of the lunar cycles to the equinoxes, however, might seem quite mysterious and perhaps that was what gave rise to the need for religious interpretation and the construction of stone circles.
I like J R R Tolkien's Hobbit calendar. Every year has 13 months of 28 days, so days of the month always fall on the same day of the week. That accounts for 364 days. New Year's Day is a special day that's independent of the weekdays and every fourth year there's an extra "leap day" that follows after New Year's Day.
