The criteria is that on the New Moon day, if the moon is born before sunset at Makkah and moonset is after sunset then the month start on that night. First day of the month falls on the next day, otherwise wait for another day.
Dr. Zaki A. Mostafa of King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia, published an article,"Lunar Calendars: The New Saudi Arabian Criteria" in SAO/NASA Astrophysics Data System (ADS) Journal of The Observatory, Vol 125, p. 25-30. In conclusion of this article, he says, "Saudi Ummul-Qura criterion depends upon the probability of seeing the crescent rather than the capability (or visibility), that reduces the errors of starting the month before the conjunction or of beginning the month two days after the conjunction."
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