moon sighting

Translation excerpt from Sura Baqarah
They ask you (O Muhammad SAW) about the new moons. Say: These are signs to mark fixed periods of time for mankind and for the pilgrimage. It is not Al-Birr (piety, righteousness) that you enter the houses from the back but Al-Birr (is the quality of the one) who fears Allâh. So enter houses through their proper doors, and fear Allâh that you may be successful.
Verse 189

Excerpt of tafsir of this verse from Tafsir Ibn e Kathir

It is narrated in Musannad Abd ur Razzaq by Hazrat Abdullah ibn e Umar R.A ,from Seal of Prophets Syedna Muhammad Salla'l la ho alaye hi wasallam :
Allah has made the moon for the people to know the time.Fast by its sight,celebrate eid with its sight,if you are unable to sight the moon due to cloud (or other weather conditions) then complete (the month of) 30 days

Authenticity
Imam Hakim R.A has declared it sahih.This hadith is narrated in other books of hadith as well and the same topic has been narrated by Mola Ali KaramUllah Wajhu hu RaziAllah An'hu in a mauquuf tradition.
(Reference :Tafsir ibn e kathir)