This Scriptural Calendar study gives a summary of the conclusions that are explained on this website.
The dark conjunction phase of the moon declares the New Moon day and new month, which starts the dawn after the conjunction.
The New Moon Day is the 1st day of the Biblical calendar. Then the 7-day week pattern is followed, resulting in the Sabbaths falling on the 8th, 15th, 22nd and 29th of the Biblical calendar.
If the New Moon Day is on a Thursday of the modern Gregorian calendar, then the Sabbaths for that month will also be on Thursday.
A day starts at dawn, when the Sun begins to take rule over the sky. A Sabbath or Feast Day is observed from dawn to dust (even to even), during the day time; except on the Feast of Atonement, on which one is to observe it from dust on the 9th day until dusk on the 10th day.
The dark conjunction that leads to a full moon after the Spring Equinox is the start of the new Biblical year.
If after the 12th month, the next dark conjunction leads to a full moon before the Spring Equinox, then a 13th month is observed.
A 13th month has to be added 7 of 19 years, to keep the Feasts in the correct season; as the lunar year is shorter than the solar year.