Traditional in highly religiously-influenced Muslim cultures months, included Ramadan, began when the local imam for Sunnis or local highest religious authority figure for Shia spotted the waxing moon. If that night is cloudy then there is a split in thought. Since astronomy has been well understood in Muslim cultures most traditional localists will automatically declare the next night (night two of the waxing moon) as the start of Ramadan. The thinking is God has granted the faithful an extra day before the long fasting month. A small minority of traditional localists will wait until they see the moon again.
Revolutionary Mecca-only Universalists
Mecca has been the focus point of Islam since Muhammad fled Mecca in AD 622 (year 1 of the Islamic calendar). Recently revolutionary Islamic sects like Salafists and Wahabbis have been pushing for a global Mecca-only as opposed to the traditional Mecca-primary implementation of Islam. Geographically this has the implication that Ramadan does not begin for anyone until the waxing moon is spotted in Mecca.
Scientific universalists have been recently gaining ground in the Muslim community but have a very long historical presence in Islam. These people believe Ramadan begins at the start of the waxing moon no matter if the moon is seen or not. They state that Islam encourages science as a way to explain God and that astronomical knowledge is religiously valid way to determine the start of the holy month. Traditionalist and revolutionary Muslims disagree though.