The current definition of the Jewish calendar is generally said to have been set down by the Sanhedrin president Hillel II in approximately C.E. 359. The original details of his calendar are, however, uncertain. The Jewish calendar is used for religious purposes by Jews all over the world, and it is the official calendar of Israel. This is a complicated goal, and the rules for the Jewish calendar are correspondingly fascinating. Lunisolar calendars use months to approximate the tropical year.
Examples are the Jewish and Chinese calendars.
The big question is how to do this. A simple method is to just base it on nature. In ancient Israel, the religious leaders would determine the date for Passover each spring by seeing if the roads were dry enough for the pilgrims and if the lambs were ready for slaughter. If not, they would add one more month. An aboriginal tribe in Taiwan would go out to sea with lanterns near the new moon at the beginning of spring.