On the Shabbosim before Rosh Chodesh we "Bench" the new month between Shacharis and Mussaf (like here).
Why do we do this? What's the source for it?
The earliest source seems to be Machzor Vitry (by Rabbeinu Simcha of Vitry, one of Rashi's disciples), sec. 190. He states that this is done so that:
people will be clear on when the upcoming holidays are ("takkanas hamoados")
people will know when Rosh Chodesh itself is, which is important for:
a. reciting Mussaf
b. reciting Hallel
c. women not working (in keeping with a custom recorded in Shulchan Aruch, Orach Chaim 417:1).
Aside from this, I've also seen a statement by the Rogatchover Gaon (cited here), that it is in memory of the formal declaration of Rosh Chodesh by the Sanhedrin.
A really intriguing answer is brought in the Aruch Hasulchan (417:6-9) That it is based on a Yerushalmi in Sanhedrin 5:3 Where it brings a case where 2 people came to testify about a crime and one says it was the Second day of the Month another says it was the third and we cant disprove their testimony because maybe one knew that the Month had an extra day and the second did not, there Reb Yosa says "like me when once I did not say Mussaf. I did not know when Rosh Chodesh was".This could be construed to mean he missed it because he did not Daven Mussaf the Shabbos before in shul so that's why he missed Rosh Chodesh Because he missed Rosh Chodesh bentching and Hence Mussaf thereafter a semi proof for our Minhag of saying it a shabbos before. More of what was said earlier cant be found in the Levush in Siman 481 says "The custom is to bless every new month on the Shabbos before Rosh Chodesh so the Matter is Publicized and everyone knows on what day Rosh chodesh will be". That is since there are more people in shul on Shabbos it is the optimal time.