On Rosh Hodesh, during the three prayers, Arbith, Shahrith, and Minha we say Ya'aleh WeYabo. This excludes, of course, Mussaf which exists on Rosh Hodesh.
If, during 'Arbith, you forgot to say Ya'aleh WeYabo, you do not repeat the 'Amidah. The reason for that is that the Sanhedrin never announced Rosh Hodesh at night. Even if they were aware that that particular night would, in fact, be in fact Rosh Hodesh, it was never announced at night. So therefore, if at night you forget to say Ya'aleh WeYabo in the 'Amidah you do not repeat it, even if Rosh Hodesh is two days. However, if you did not say it for Shahrith or Minha, you have to go back and say it, in accordance with the rules of going back, which we will talk about on another occasion. And if you finished the 'Amidah before you remembered, you have to repeat the 'Amidah.
Just one point about repeating the 'Amidah, anytime you have to repeat the 'Amidah, you do not say "Hashem Sefathai Tiftah" the second time, you just go back to Barukh of the first Berakha.
(See Ben Ish Hai, Shanah sheniah, Oth Yod Beh)
