God gave us scientific knowledge to determine exactly when a lunar month will begin and end. Astronomers have this knowledge precisely calculated and we can compute the day Ramadan will begin (or end) for a particular year months and years in advance. Lunar calendars are printed and people conduct business and trade in middle eastern countries without any uncertainty. God says in the Quran:
[Quran 10:5] He is the One who rendered the sun radiant, and the moon a light, and He designed its phases that you may learn to count the years and to calculate. GOD did not create all this, except for a specific purpose. He explains the revelations for people who know.
[Quran 2:189] They ask you about the phases of the moon! Say, "They provide a timing device for the people, and determine the time of Hajj." It is not righteous to beat around the bush;* righteousness is attained by upholding the commandments and by being straightforward. You shall observe GOD, that you may succeed.
We do not try to physically see the sun's position when it is time to pray our Contact Prayers (Salat). The sun, earth and moon follow precise orbits (21:33). Similarly, there is no need for trying to sight the crescent of the moon to start fasting. Any observatory or astronomy center should have that information for your area. Some almanacs, magazines or newspapers also report the times for the phases of the moon.
To determine when one should start fasting, compare the time the new lunar month begins with the time of sunset, the beginning of a day in the Islamic calendar. If the new moon time for the month of Ramadan is before the sunset, one starts fasting the next day at dawn (fajr). However, if the new moon time is actually past the sunset, then that particular night is considered to belong to the last day of the previous month (Sha’ban).
More information on the lunar calendar as it relates to Ramadan (note: the Ramadan dates in this article are of 1999; please see: Ramadan page for current fasting information)