How to use this table:

The year:

The Gregorian lunar almanac is a 19-year cycle which assigns an age of the moon to every day in the 19-year period.

Year one of the Gregorian cycle is any year in which the year's number is divisible by 19 without remainder.  The year 2204, for example, is year one of its cycle:  The table shows that Lunar Year 2204 begins on January 3nd, 2204.  (More precisely, at sunset on January 2nd, 2204).   Successive years of the cycle follow in order.  The year 2205 is year two:  Lunar Year 2205 begins on December 23rd, 2204  (Or more precisely, at sunset on December 22nd, 2204).   The year 2206 is year 3:  Lunar Year 2206 begins on December 12th, 2205.
 

The month:

Each year contains 12 or 13 lunar months.  Each lunar month has 29 or 30 days.

The table shows the first day of each lunar month in the Gregorian Easter cycle.  The moon is considered to be one day old on the first day of the lunar month.  This day is also called "new moon" because it corresponds, on the average, to the day on which the new waxing  crescent moon theoretically first becomes visible.

If February has 29 days, an extra day is added to month 2, making it a month of 30 days, rather than 29 days.  Month 3 then begins a day later than the date listed in the table if the date listed is a date prior to February 29th.  (This is not the only  possible way of accounting for a 29-day February, but it is the easiest.)

The last lunar month of the 19th year of the cycle has 29 days.

In the year 2299, which is the first year of the 19-year cycle and the last year in which this table is valid, an extra day is added to month 12, making it a month of 30 days, rather than 29 days.
 

The day:

Because this is a Babylonian-style lunar calendar, the day begins on sunset of the day prior to the day listed in the table.  The table shows that the first day of the first moon of year 1 of the cycle corresponds to January 2nd.  This means that the first day  of the lunar month begins at sunset on January 1st and ends at sunset on January 2nd, when the second day of the lunar month begins.
 

The Easter festival falls in the first lunar month of the year to begin on or after March 8th.  In the years 2200-2299 this is usually the 4th moon, though in year 17 of the 19-year cycle it is the 5th moon.  Easter is always the third Sunday in its lunar month.

In the Earth's Northern hemisphere, the Spring season of year 4 of the Gregorian cycle coincides with the Spring season of year 1 of the Jewish 19-year cycle, with other years of each cycle following in succession.  The Feast of Unleavened Bread for the year 5982 (year 16 of the Jewish cycle) occurs in the Northern hemisphere's springtime in the Gregorian year 2222 (year 19 of the Gregorian cycle.)

Due to differences in the time of year at which the Christian and Jewish cycles add the 13th moon of 13-moon years, the Jewish Feast of Unleavened Bread in the years 2200-2299 will, in years 3, 6, 11, and 14 of the Gregorian cycle (corresponding respectively to years 19, 3, 8, and 11 of the Jewish cycle), fall in the lunar month next after the lunar month in which the Christian Easter festival falls.  In all other years of the cycle, Easter and the Feast of Unleavened Bread fall in the same lunar month.  But though the lunar month in which the Jewish Feast of Unleavened Bread falls can be identified using the table above, the precise dates of the Feast of Unleavened Bread cannot be determined accurately from the table.  This is because the Gregorian and Jewish calendars use different rules for computing the moon's age.

References:

Explanatory Supplement to the Ephemeris and the American Ephemeris and Nautical Almanac, H. M. Stationery Office, London, 1966, fourth revised printing, 1977.

Alexander Philip, The Calendar: Its History, Structure and Improvement, University Press, Cambridge, 1921.

L. A. Resnikoff, "Jewish Calendar Calculations I", Scripta Mathematica 9, 191(1943); "Jewish Calendar Calculations II", Scripta Mathematica 9, 274(1943).