Imam Al-Nawawi's Riyad-us-Saliheen
Chapter 220
Supplication at the Sight of the Crescent (At the outset of Every Lunar Month)

1228.  Talhah bin  Ubaidullah (May Allah be pleased with him) reported: At the sight of the new moon (of the lunar month), the Prophet (sallallaahu ’alayhi wa sallam) used to supplicate: "Allahumma ahillahu `alaina bil-amni wal-iman, was-salamati wal-Islam, Rabbi wa Rabbuk-Allah, Hilalu rushdin wa khairin (O Allah, let this moon appear on us with security and Iman; with safety and Islam. (O moon!) Your Rubb and mine is Allah. May this moon be bringing guidance and good).''
[At-Tirmidhi].

Commentary:  After sighting the moon, one should recite the prayer which was recited by the Prophet (sallallaahu ’alayhi wa sallam). The prayer cited in the text of this Hadith is one of them.