Sahih al-Bukhari 1906
Sahih al-Bukhari · Book 30: Fasting · "Start observing Saum on seeing the crescent of Ramadan, and stop on seeing the crescent (of Shawwal)."
Narrated `Abdullah bin `Umar:
حَدَّثَنَا عَبْدُ اللَّهِ بْنُ مَسْلَمَةَ ، عَنْ مَالِكٍ ، عَنْ نَافِعٍ ، عَنْ عَبْدِ اللَّهِ بْنِ عُمَرَ ـ رضى الله عنهما ـ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم ذَكَرَ رَمَضَانَ فَقَالَ " لاَ تَصُومُوا حَتَّى تَرَوُا الْهِلاَلَ، وَلاَ تُفْطِرُوا حَتَّى تَرَوْهُ، فَإِنْ غُمَّ عَلَيْكُمْ فَاقْدُرُوا لَهُ " .
Allah's Messenger (ﷺ) 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).