Establishing exactly when a lunar month begins has never been a trivial calculation, and the different solutions traditions have reached still shape how the new moon is kept today. The astronomical new moon, the instant the moon sits between earth and sun with no illuminated face visible from earth, is not itself observable, and no tradition bases its calendar directly on it. Islamic practice historically required an actual sighting of the young crescent low in the west after sunset, a requirement that keeps the start of Ramadan and the date of Eid dependent on weather, latitude and who is doing the looking, so that neighbouring countries, and sometimes neighbouring mosques, can announce different dates in the same week. Astronomical calculation of when the crescent becomes visible in principle is now available and used by some communities and rejected by others as a departure from the sighting requirement stated in hadith.
The Jewish calendar solved the same problem differently and earlier. Its months were originally fixed by testimony of witnesses before a rabbinic court, but a fixed arithmetic calendar, attributed to Hillel II in the fourth century, replaced observation with calculation centuries ago, so Rosh Chodesh today is announced from a mathematical table rather than a sighting.
The Hindu lunisolar calendar keeps amavasya by calculation as well, adjusted regionally so that the timing of the same dark-moon observance can differ by a day between communities using different regional almanacs. Modern Pagan practice, having no inherited authority to defer to, generally follows whatever astronomical almanac or app the practitioner trusts, which makes it the only one of the four with no institutional dispute attached to the date at all.