According to Shulchan Aruch you are allowed to say Bircat HaLevanah until fifteen days from the hour of Molad (look in a Hebrew calendar for the time). If that time passed, then one may read the Bracha from the Gemara as if you are learning it but without any Shem Hashem or the Melech Haolam.
Explanation:
The Gemara in Sanhedrin(41b)says R’ Yochanan said until when can we say blessing on the new Month, until it becomes unblemished. How much is that? Rav Yehuda says seven days. Nehardai say until sixteen days. They both follow the opinion of R’ Yochanan. One understood he meant it shouldn’t be a crescent and one says it should be like a bellows.
Rashi explains Rav Yehuda’s opinion it’s damage should be repaired look like a bow with its string; a semicircle. Nehardai understood that it should be unblemished like a bellows, meaning like a ball, a sphere.
The Ram “a MiPano explains that there is no actual argument between Rav Yehuda and Nehardai, rather Rav Yehuda is giving the time when one can start saying Bircat HaLevanah, and Nehardai are telling when you cannot say it anymore.
The Rambam ruled like Nehardai, that one can say the Bircat HaLevanah until sixteen days into the month, and so ruled the Shulchan Aruch OH 426:3.
There is a big disagreement among the later Poskim if sixteen days includes the sixteenth or it is not including the sixteenth(fifteen days only). The Tur (OH 426) understood that it does not include the sixteenth day. However, the Shayrei Knesset Hagedolah quotes a Shita in Sanhedrin in the name of Rabbeinu Peretz and the Meiri the it includes the sixteenth.
The Rem”a (426:3)ruled like the Mahari”l that fifteen days means half a month and a month is twenty-nine days, 12 hours , and seven hundred ninety-three Chalakim (29d12hrs793ch). Therefore, one can say the bracha until fourteen days eighteen hours and three hundred ninety-six and a half Chalakim (14d18hrs396.5ch).
The Shulchan Aruch ruled like the Tur, that it does not include the sixteenth day, but we count from the day of the Molad (time when the Moon reappears) not the hour. The Magen Avraham (ibid 12) comments that it seems that the Shulchan Aruch the the only starts counting form the beginning of the day of the Molad, which would be more stringent than the Rema and the Rema seems to try to be more stringent than the Shulchan Aruch. Therefore, the Magen Avraham decided that the Shulchan Aruch also counted from the time of the Molad, and so understood the Mishna Berura (426:17)
For example, if the Molad fell out at 12:00 noon on Yom Rishon, then one may say the bracha on Yom Sheni two weeks later since a full fifteen days hasn’t passed from the time of the Molad. This comes out into the sixteenth day.
Many Poskim say that if one missed the time one should say the bracha without Hashem’s name or the words Melech Haolam. The Mateh Efrayim (581-Elef Hamagen 22) writes that one who didn’t say Bircat HaLevanah on time should take Gemara Sanhedrin(42a) outside and start with the statement “HaRoeh Levana B’Chidusha Omer Baruch…the rest of the bracha.”
R’ Ovadiah Yosef ZT”L ruled (Yabia Omer 6:38) that one should still not say Hashem’ s name even if reading the Gemara and you only have until fifteen days from the hour of the Molad.
