What is the hardest thing I need to be able to do to use this method?
You need to be able to divide a number from 0 to 34 by 7 and take the remainder. If you remember the sequence 0, 7, 14, 21, and 28, you can take the largest of those and subtract it from the number, and you get the remainder directly.
Method from 1900 to 2199
Remember the current values of M and N1. For each advance of year, increase M by 19 or decrease it by 11, whichever keeps it in the acceptable range 0 to 29. If the new value happens to be 25, subtract one.2 For each advance of a year, increase N by one, or by two if the new year is a leap year. If N goes over 6, subtract 7, to keep it in the acceptable range 0 to 6.
Calculate A3. A is the same as M, unless M is 28 or 29, in which case A is one less than M.
Calculate B. B is A plus N.
Calculate C. C is the remainder of division of B by 7.
Calculate D. D is A minus C.
Calculate the date of easter. It is either D minus 3 in April, or D plus 28 in March.
25.4.
1N is the same N as used for knowing what day of the week it is in Conway's doomsday method I've described on another page.
2This happens every 19 years, in years exactly divisible by 19, which are 2014, 2033, 2052, 2071, 2090, 2109, 2128, 2147, 2166, and 2185.
3A is the number of days after March 21 (the spring equinox according to the church) of the first full moon (again according to the church). The remaining steps are just to get the next Sunday from that, but that can be achieved in other ways too, like using the doomsday method. The approximations in these rules of the spring equinox and the moon cycle can be off from reality by a day or two, but easter is defined by these rules, not the sun and the moon. But if you don't mind the small error, this way you can get the phase of the moon for any date. You can go forwards or backwards by a year or so from the spring full moon by steps of 29,5 days without introducing too much extra error.
What if I lose my place or want to calculate a year a long way from now?
Divide the year by 19 and the remainder is G. Divide 24 + 19*G by 30 and the remainder is M.
Divide the year by 400 and the remainder is Z. Divide Z + Z/4 - Z/100 + 2 by 7 and the remainder is N.
Other centuries
The 19-year cycle of M starts from 24 between 1900 and 2199. In 2200 it starts from 25. The formula for the initial value in a given century is 15 + 3*century/4 - (5+8*century)/25. Divisions are rounded down to the nearest whole number. When the result is 30 or more (which happens after 3400), it is divided by 30 and the remainder taken.
The handling when M is 28 is different in different centuries. Only if M is 28 in the last 8 years of the cycle, is one subtracted to get A of 27. This is the same as the year divided by 19 having a remainder of 11 or more.
This happens to be those centuries where the cycle-initial M multiplied by 11 and divided by 30 gives a remainder of 19 or more, so after 2199 the first time this happens is in 3100.
The first easter which was calculated anywhere with these rules was in 1583. Before that, the cycle of M always started from 15, and the leap year system was simpler, every fourth year was always a leap year.