When seeing the new moon, one should recite the following dua once:
هِلَالُ خَيْرٍ وَرُشْدٍ
(O Allah! Make the crescent of this month) a crescent of goodness and guidance (i.e. a crescent that brings goodness and guidance with it).
Then, one should recite the following dua thrice:
اللَّهُمَّ إِنِّي أَسْأَلُكَ مِنْ خَيْرِ هَذَا
O Allah, I ask You for the goodness of this (new moon)
Thereafter, one should recite the following dua thrice:
اللَّهُمَّ إِنِّي أَسْأَلُكَ مِنْ خَيْرِ هَذَا الشَّهْرِ، وَخَيْرِ الْقَدَرِ، وَأَعُوذُ بِكَ مِنْ شَرِّهِ
O Allah, I ask You (to grant me) the goodness of this month and the goodness that has been decreed in it, and I seek Your divine protection from its evil (i.e. from the evil of this month and from the evil that has been decreed in it)
وعن رافع بن خديج قال: كان رسول الله صلى الله عليه وسلم إذا رأى الهلال قال: هلال خير ورشد. ثم قال: اللهم إني أسألك من خير هذا ثلاثا، اللهم إني أسألك من خير هذا الشهر، وخير القدر، وأعوذ بك من شره ثلاث مرات. رواه الطبراني، وإسناده حسن. (مجمع الزوائد، الرقم: 17147)
Hazrat Raafi bin Khadeej (radhiyallahu ‘anhu) reports that Rasulullah (sallallahu ‘alaihi wasallam) would recite the abovementioned dua when he would see the crescent (of the new month).