Prophet (SAW)'s Prayers When sighting the new moon

Dua at the time of sighting the moon:

أَعُوذُ بِاللَّهِ مِنْ شَرِّ هَذَا

"I seek refuge in Allah from this (its) evil."

Dua when sighting the new moon:

اللَّهُمَّ أَهِلَّهُ عَلَيْنَا بِالْيُمْنِ وَالْإِيمَانِ وَالسَّلَامَةِ وَالْإِسْلَامِ وَالتَّوْفِيقِ لِمَا تُحِبُّ وَتَرْضَى رَبِّي وَرَبُّكَ اللَّهُ

"O Allah, let this moon (month) pass over us with blessings, Iman, safety, and in the belief of Islam. Grant us the ability to act on the actions that You love and Pleases You. (O moon) My Lord and Your Lord is Allah". (Hisnul Hasin from Ibn Habban)