Easter takes place on the first Sunday after the first full moon after the spring equinox.
Except not exactly, because spring only occurs for up to half of the earth at a time. Since the death and resurrection of Jesus happened in the northern hemisphere, and both because of a thematic link between the resurgence of plant life in the spring and the Resurrection and because this should line up roughly with the Jewish date of Pesach, near which the events actually occurred, the equinox referred to is the northern Spring equinox, which happens near the end of March, so…
Easter takes place on the first Sunday after the first full moon after the March equinox.
Except not exactly, because the equinox is an astronomical instant in time when the earth's axial tilt exactly forms a right angle with the line between the earth and the sun. This usually happens on March 20, varying up to one day either way, but the western churches have defined it to always be on March 21 no matter what actually happens astronomically. This is where the differences between the western and eastern churches arise, as the eastern churches still use the Julian calendar, where the equinox is currently defined as April 3 and will continue to drift further into the year over extended periods of time. So…
Easter takes place on the first Sunday after the first full moon after the Gregorian March 21 in the west and the Julian April 3 in the east.
Except not exactly, because the full moon also really happens just at one instant when the moon and sun are opposite each other from our point of view, making the near side completely lit. Due to time zones, this instant can be recorded with over 24 (yes, over) different times on the clock and multiple dates depending on what location on the earth you measure time from. This is why each church uses slightly different complicated math to calculate an agreed-upon date for the full moon as an offset applied to a calculation for the new moon called the ecclesiastical full moon. Again, no matter what the moon actually looks like, that is the full moon used in the definition. So…
Easter takes place on the first Sunday after the ecclesiastical full moon immediately following the Gregorian March 21 in the west and the Julian April 3 in the east.
And, of course, this is subject to even further exceptions and arguments throughout the centuries and may be changed slightly or completely in the future. That is why, for now, most people are content to let their calendar, prayer book, hymnal, or missal tell them what date will be considered Easter and plan accordingly. The important thing is celebrating the joy of our Lord's resurrection as the promise of our own, and for anything more it is always a good idea to ask your pastor or priest.
A far more complete and complex explanation is available here: https://en.wikipedia.org/wiki/Date_of_Easter.