Sighting the new moon determines the beginning and end of Islamic appointed times of rituals

Q 2: How is the first day of every month determined, and how do the scholars in the Kingdom of Saudi Arabia know the number of the days of every Month when preparing the annual lunar calendar The answer to this question is paramount for us due to huge disagreement on how to determine the first day of the month. This confusion causes some Muslims sometimes to fast one or two days before or after Ramadan. Some of them celebrate `Eid-ul-Adha (the Feast of the Sacrifice) and sacrifice their animals on the Day of `Arafah. The only reason for this confusion is the lack of sound knowledge regarding the method of determining the first day of the month and the number of days in each month. Moreover, the new moon does not clearly appear to us on the first day of the month. (Part No. 9; Page No. 19

A: The beginning and end of Islamic appointed times of rituals, such as Ramadan, Hajj (pilgrimage), and other rituals are determined by sighting the new moon with the naked eye. It is not permissible to rely on predetermined calculations and calendars which are made for the next ten years. This ruling is based on Allah's (Exalted be He) Saying: They ask you (O Muhammad صلى الله عليه وسلم) about the new moons. Say: These are signs to mark fixed periods of time for mankind and for the pilgrimage and on the Prophet's (peace and blessings of Allah be upon him) saying: Observe the fast when you see it (the new moon) and break the fast when you see it (the new moon). If the sky is overcast, complete the month of Sha'ban as thirty days. (Related by Al-Bukhari and Muslim in their two Sahihs)May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.