Dua on seeing the new moon:

اللَّهُ أَكْبَرُ، اللَّهُمَّ أَهِلَّهُ عَلَيْنَا بِالَأمْنِ وَالإِيمَانِ، وَالسَّلَامَةِ وَالِإسْلَامِ، وَالتَّوْفِيقِِ لِمَا تُحِبُّ رَبَّنَا وَتَرْضَى، رَبُّنَا وَرَبُّكَ اللَّهُ

Allaahu 'Akbar, Allaahumma 'ahillahu 'alayna bil'amni wal'eemaani, wassalaamati wal-'Islaami, wattawfeeqi limaa tuhibbu Rabbanaa wa tardhaa, Rabbunaa wa Rabbukallaahu.

Allah is the Most Great. O Allah, bring us the new moon with security and Faith, with peace and in Islam, and in harmony with what our Lord loves and what pleases Him. Our Lord and your Lord is Allah.

Ref: At-Tirmizi 5/504, Ad-Darimi 1/336. (Albani: Saheeh with its shawaahid)