Begin and end Ramadan fasting upon sighting the crescent moon or estimate it

Messenger of Allah 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).

أَنَّ رَسُولَ اللَّهِ ﷺ ذَكَرَ رَمَضَانَ فَقَالَ لاَ تَصُومُوا حَتَّى تَرَوُا الْهِلاَلَ وَلاَ تُفْطِرُوا حَتَّى تَرَوْهُ فَإِنْ غُمَّ عَلَيْكُمْ فَاقْدُرُوا لَهُ