Many Rishonim hold that the time for Birkat HaLevanah starts on the first day that the moon is visible, and that the earlier one says the blessing the better (Rambam, Hilchot Berachot 10:17; Rosh; and others). Several poskim, however, maintain that it is preferable to wait until the moon increases a bit, when it is possible to benefit from its light. Some say one should wait until three whole days pass, for that is when the moon’s light becomes substantial (R. Saadia Gaon, Talmidei Rabbeinu Yonah). Others say seven days must pass, because that is when one can truly benefit from its light (Rama of Panow, Responsa 78). According to some of the greatest Kabbalists – most notably, R. Yosef Gikitilla – one should wait seven days, for esoteric reasons. They explain that the renewal of the moon’s light alludes to man’s renewal, and whenever there is a new development, there is concern that the Attribute of Justice might prosecute and hinder the new growth. Therefore, it is proper to wait seven days, like the seven days of Creation, for by then the moon’s light has stabilized and the Attribute of Justice can no longer wage war against the new beginning.
Sefardim and Hasidim are accustomed not to recite the blessing before the seventh of the month (Shulchan Aruch 426:4), while Ashkenazim say it after three days (Bach, Mishna Berura 426:20). In practice, the custom is to bless the new moon on Saturday night, in order to say the blessing joyously, while wearing nice clothing. Thus, practically speaking, Ashkenazim and Moroccan Jews recite Birkat HaLevanah on the Saturday night that follows three whole days after the molad (the “rebirth” of the moon), while Sefardim and Hasidim say it on the first Saturday night after the seventh of the month.
There is a dispute regarding how to act when the seventh of the month begins on a Saturday night, but seven complete days from the time of the molad[168 hours] have not yet passed. Some authorities insist that we postpone the blessing until the next night, or the next Saturday night, which will fall out on the fourteenth of the month (Rashash, Rebbe Zalman of Liadi, Kaf HaChaim 426:61). Others contend that even if a few hours remain until the end of the seventh day from the molad, one may say Birkat HaLevanah(Knesset HaGedolah, Yechaveh Da’at 2:24). If people from different ethnic backgrounds pray together, and the seventh of the month falls out on a Saturday night, it is proper for everyone to recite Birkat HaLevanah, according to the opinion of the majority of poskim.
One who failed to say Birkat HaLevanah by the seventh of the month can say it until the end of the night of the fifteenth, because the moon is still full until then. Afterwards, it begins to wane, and therefore, the blessing cannot be said from the night of the sixteenth and onward (Shulchan Aruch 426:3).
Preferably, one should take into account the opinion of the Maharil, who holds that one may not say Birkat HaLevanah after half of the moon’s cycle has elapsed (14 days, 18 hours, and approximately 20 minutes from the time of the molad). This time rarely passes the beginning of the night of the fourteenth. By the night of the fifteenth, the moon’s cycle sometimes reaches the halfway mark, and sometimes not (Rama 426:3, Kaf HaChaim 53). Nevertheless, in practice, one who did not say the blessing by the fourteenth may say it until the end of the night of the fifteenth (Biur Halachah 426:3, Yabi’a Omer 8:42).
 See Beit Yosef and Shulchan Aruch 426:4, Bach and Mishna Berura ibid., Kaf HaChaim 61, Sefer Kiddush Levanah 3:1-2. Many Rishonim hold that the blessing should be said immediately upon the moon’s reappearance [at the beginning of the month]. R. Ya’akov Roke’ach writes in Shulchan Lechem HaPanim that this seems to be the opinion of R. Amram Gaon, Behag, Rif, Rambam, Rosh, and others. The Bach points out that the Talmud implies that one should not say Kiddush Levanah after the seventh day. The Rambam, as well, indicates that it is preferable to say it as early as possible. On the other hand, some poskim infer from Tractate Soferim (20:1) that one should not bless the new moon until it is possible to benefit from its light. Talmidei Rabbeinu Yonah, R. David Avudraham, the Kolbo, and others espouse this viewpoint. This is also the practical implication of the discussion cited above in note 23. According to Kabbalah, one should say the blessing after seven days. In practice, the custom of Ashkenazim is to bless the moon after three days have passed. This is also the custom of the Jews of Morocco and other North African communities (so writes Rabbi Mashash and many others). The majority of Sefardim, based on Kabbalah, as well as the Hasidim, are accustomed to reciting the blessing after seven days. Moreover, some Ashkenazim follow this custom l’chatchillah (preferentially), as the Chatam Sofer (Orach Chayim 102) and Aruch HaShulchan (426:13) write. Nonetheless, when the seventh falls out on a Saturday night, it seems preferable to recite Birkat HaLevanah then, even if seven complete days from the molad have not yet passed. Thi I because the moon’s light is already abundant and part of a day is regarded as an entire day. All the more so seeing that it is Motzei Shabbat, a joyous time which is suited for Birkat HaLevanah. Besides which, several poskim hold that one should recite the blessing as early as possible (Ramban and his adherents), while others assert that one should not say it later than the seventh of the month (Bach). Therefore, it is proper to say it on the night of the seventh, even if seven complete days have not passed since the molad. This is how the Knesset HaGedolah, Rama of Panow (78), Nahar Mitzrayim, Eliyah Rabbah, Eshel Avraham of Buchach, Maharsham, and others conclude (see Sefer Kiddush Levanah 3:8, with notes 27 and 29; Yechaveh Da’at 2:24).