Hadith: Observe the fast when you see it and break the fast when you see it, but if the sky is overcast and you cannot see it, then act on estimation

عن عبد الله بن عمر رضي الله عنهما قال: سمعت رسول الله صلى الله عليه وسلم يقول: «إذا رَأَيْتمُوه فَصُومُوا، وإذا رَأَيْتُمُوه فَأفْطِروُا، فإن غُمَّ عليكم فَاقْدُرُوا له».
[صحيح] - [متفق عليه]

‘Abdullāh ibn ‘Umar (may Allah be pleased with him) reported: I heard the Messenger of Allah (may Allah's peace and blessings be upon him) saying: "Observe the fast when you see it (the new moon of Ramadan), and break the fast when you see it (the new moon of Shawwāl), but if the sky is overcast and you cannot see it, then act on estimation (by counting Sha‘bān as 30 days)."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

Rulings of the noble Shariah are built on principles which are immune to modification unless there is certainty. For instance, the basic rule is that one is not required to fast as long as Sha‘bān is still going on. This ruling stands as long as the thirty days of Sha‘bān have not passed yet, the thing that signals its end, or if one sights the crescent which signals the beginning of Ramadan. For this reason, the Prophet (may Allah's peace and blessings be upon him) made the fast of Ramadan and the break of its fast contingent on seeing the crescent. In case it is cloudy, rainy, or the like, Sha‘ban is to continue its thirty days, because in principle it lasts thirty days unless there is a certainty proving otherwise. The Shariah rule states: "The ruling stands on its original case."