How I determine New Moon day:
Conjunction is the evening when the moon cannot be seen as the sun is directly upon the other side of it when compared with our location on earth. The new moon needs to be seen to declare new moon day. There can only ever be a maximum of two new moon days in a month.
The day after the last Sabbath the new moon may not be seen. This day becomes the 30th day of the month. The following day becomes the 1st of the month.
If the new Moon is seen on the day after the last Sabbath, that day is the 1st of the month.
How to work it out:
1) The last Sabbath is upon the 29th day.
2) Upon the following day in the evening, look for the first visible crescent. If it is seen, that day is the first day if the month.
3) If the first visible crescent is not seen, that month has 30 days and the first day is the day after.