It is recommended that whoever sights the crescent (Hilal) of Ramadan, or any other month for that matter, or is informed about the new crescent, should say:
اللَّهُمَّ أَهْلِلْهُ عَلَيْنَا بِالْيُمْنِ وَالإِيمَانِ وَالسَّلاَمَةِ وَالإِسْلاَمِ رَبِّي وَرَبُّكَ اللَّهُ
Allahu Akbar, Allahumma ahillahu 'alaina bil yumni wa Iman, Was Salaamata wal Islam, Ribbi wa rabbika illah. (Tirmidhi)
Meaning: Allah is Greatest. O Allah, make it the beginning, the beginning of prosperity, faith, peace, and total submission to Allah. Your Lord and mine are Allah.
Also, it has been reported from Ali bin Abi Talib (raa) that the Messenger said: "If you witness the crescent of the new month, say:
Allahu Akbar (three times) Al-hamdu Lillah. Alladhi Khalaqani wa Khalaqaka, wa qaddara laka manajil wa ja'alaka ayatna lil 'ala meen. (Naylul Awataar)
Meaning: Allah is Greatest. (three times) praise be to Allah who created me and you and decreed for you the phases and made you a sign for the universe.