For starters, (most) Catholics use the Gregorian Calendar in order to calculate Easter while the Orthodox (and some Eastern Catholics) use the Julian Calendar.
The canons of Nicaea state that Easter should occur the first Sunday after the first full moon after the vernal equinox. The vernal equinox is nominally stated to be March 21. The actual date can vary due to the inability of the relatively arbitrary human calendar system to fully mesh with the astronomical observation we call the equinox. However, March 21 is the starting point for both calendars. Since the Julian calendar presently has a 13 day difference from the Gregorian calendar, the date of Easter is bound to be off most years between the two. Considering that the equinox is a solar event and the full moon a lunar event, the two are not usually going to coincide, but sometimes do (as it will again in AD 2010 and 2011).
As far as the actual calculations go, there's is an article on wikipedia entitled Computus
which I think does a decent job in setting out the rules for each calendar's computation of the date of Easter.
Hope this helps.