the judge would not confirm the beginning of the month of Ramadan and announce to the general public to commence fasting--relying solely upon their testimony. However, if just one upright Muslim, who has the conditions listed above satisfied in him, testifies to the judge that he saw the crescent, the judge would confirm the beginning of Ramadan for the next day.

This is for the hadith related by Abu Dawud from the route of ^Abdullah Ibn ^Umar who told the Prophet he had sighted the crescent and so the Prophet fasted the next day and ordered the others to fast as well.
Be warned of those who determine the month of Ramadan relying upon astronomical calculations.