Months are either 29 or 30 days long and begin with the first sighting of the moon (visible crescent) at sundown after the new moon.
The observation of the moon or equinox is determined by the Sundown time at Jerusalem, where the temple was.
The first day of the first month commences on the evening that the first visible crescent that can be sighted, following the spring equinox.
The equinox, as with the full moon, is determined to have started at sunset after it has already occurred.
There are twelve or thirteen months in the Biblical year. The thirteenth month is inserted after the twelfth when the next month begins before the Spring equinox.
When observing the moon to determine the next month, the observation is only made on the 29th
day of the month, and it determines whether there will be a 30th day in the current month.
Beginning in the year 2513 (the year of the Exodus), in the first six months of the year, the months alternate between 30 and 29 days length.
There is no observation of the moon until the beginning of the eighth month. The seventh to twelfth
months (or thirteenth if needed) can be either 29 or 30 days.
The years from 0 to 2512, the beginning day of all the months are determined by the observation of the moon.
Before the exodus in 2513, the calendar is getting more and more speculative. We do not know when a year would begin, so
labeling the months of a year (1st month, etc) is just speculative. I'm reasonably sure the months are accurate to within
a couple of days back to the year 0 (4046 BC), I just can't say for sure what any month is in a year. Based on the chronology of
Scripture, I can reasonably say that creation occured in year 0 of the Biblical calendar (4046/4045 BC Julian), but I
cannot specify when creation actually occured (other than it began on a Sunday).
The first day of a year in this calendar is just a calculated probability/possibility that the moon could be observed.
If on the 29th, the moon would be visible, but is obscured by the atmospheric conditions (weather),
there will be a 30th day. If this happens more than one month in a row, the beginning of the year can be delayed
a day or more from what this calendar shows.
In the year 31 AD, this calendar is adjusted with the assumption that the year was delayed for two days
because of the above mentioned possibility. This is necessary to align the 14th day of Nisan (The first month)
to Friday, April 27 (Julian), as the crucifixion of Christ.