The month begins when the new crescent is seen, and who has to see it, from where, and whether calculation may substitute, are questions that produce visible annual disagreement.
Classical practice requires observation of the hilal, the new crescent, by credible witnesses, reported to an authority who declares the month begun. Because the crescent's visibility depends on the observer's longitude, on the moon's altitude and elongation at sunset, and on atmospheric conditions, two places can legitimately differ by a day.
Two positions then divide jurists. One holds that a sighting anywhere in the Muslim world obliges everyone, global sighting. The other holds that each region follows its own, local sighting. Both have classical support. Different countries follow different rules, some countries follow Saudi announcements and others do not, and communities within a single Western city routinely begin and end the month on different days because they follow different authorities.
Calculation has been increasingly accepted. The Fiqh Council of North America adopted an astronomical criterion in 2006 and the European Council for Fatwa and Research followed in 2007, both arguing that the requirement is knowledge of the month's beginning, for which the classical method was the available instrument rather than the object. Others hold that the sighting is itself the requirement.
The resulting variation is up to about two days globally. Eid, ending the month, is affected the same way, which means families and mosques in one city can celebrate on different days, a recurrent and much-discussed source of friction.