Sahih Bukhari Volume 3, Book 31, Number 130: Narrated Abdullah bin Umar: Allah's Apostle mentioned Ramadan and said, "Do not fast unless you see the crescent (of Ramadan), and do not give up fasting till you see the crescent (of Shawwal), but if the sky is overcast (if you cannot see it), then act on estimation (i.e. count Sha'ban as 30 days)."

Crescent Visibility:

The visibility of the lunar crescent as a function of the Moon's "age" - the time counted from New Moon - is obviously of great importance to Muslims. The date and time of each New Moon can be computed exactly (see, for example, Phases of the Moon in Data Services) but the time that the Moon first becomes visible after the New Moon depends on many factors and cannot be predicted with certainty. In the first two days after the New Moon, the young crescent Moon appears very low in the western sky after sunset, and must be viewed through bright twilight. It sets shortly after sunset. The sighting of the lunar crescent within one day of New Moon is usually difficult. The crescent at this time is quite thin, has a low surface brightness, and can easily be lost in the twilight. Generally, the lunar crescent will become visible to suitably-located, experienced observers with good sky conditions about one day after New Moon. However, the time that the crescent actually becomes visible varies quite a bit from one month to another. The record for an early sighting of a lunar crescent, with a telescope, is 12.1 hours after New Moon; for naked-eye sightings, the record is 15.5 hours from New Moon. These are exceptional observations and crescent sightings this early in the lunar month should not be expected as the norm. For Islamic calendar purposes, the sighting must be made with the unaided eye (http://www.usno.navy.mil/USNO/astronomical-applications/astronomical-information-center/cres-moon-islamic).