How do they work out what day greek Easter falls on?

The Moon!

Easter is one of the Movable Feasts. It never stays on a fixed date.
What people use, to determine the date, is what is called a Lunisolar calendar. By calculating the position of the moon, they are able to identify the date.
This, Lunisolar calendar, is a complicated mathimatical forumla also explaining things like: when a leap year is (as a year is 365.25 days), or an 19-year cycle.

If you would like to learn more about the Lunisolar calendar, go to Wikipedia: Lunisolar Calendar, or New Year Festival: Lunisolar Calendar.