Perhaps because there is no prohibition against working on Rosh Hodesh, many people are unaware of the fact that Halacha regards the day of Rosh Hodesh as a minor holiday of sorts, and requires that we treat it as such. In truth, there is clear evidence that in Talmudic times people did not go to work on Rosh Hodesh. The Gemara in Masechet Megila discusses the requirement to make four Aliyot to the Torah on Rosh Hodesh, and questions why we are permitted to burden people with an extra Aliya on a weekday. The Gemara answers that people do not work on Rosh Hodesh, and so it is not inconvenient for them to remain a bit longer in the synagogue for an extra Aliya. This status of Rosh Hodesh is alluded to in the verse, "U’b’yom Simhatchem U’b’mo’adechem U’b’rosheh Hodshechem," where Rosh Hodesh is juxtaposed with "Mo’adechem" – the festivals.
As Rosh Hodesh is regarded as a holiday of sorts, one should eat a special meal in celebration of this occasion, preferably during the day (as opposed to the night of Rosh Hodesh). Hacham Ovadia Yosef rules that one does not have to eat bread on Rosh Hodesh, but one should make the meal festive by adding something that he does not eat on an ordinary weekday, such as meat or wine. The Zohar Ha’kadosh writes that just as the punishments in Gehinam are suspended on Shabbat and Yom Tob, they are suspended on Rosh Hodesh, as well. Furthermore, those who properly celebrate Rosh Hodesh receive a special dimension of Kedusha in their souls. Many people therefore have the custom to wear special garments in honor of Rosh Hodesh.
Since there is no requirement to eat bread on Rosh Hodesh, one who forgets to recite "Ya’ale Ve’yabo" in Birkat Ha’mazon on Rosh Hodesh does not repeat Birkat Ha’mazon. This is in contrast to Shabbat and Yom Tob, when Halacha requires eating bread and thus one must repeat Birkat Ha’mazon if he forgets "Reseh" or "Ya’ale Ve’yabo" on those occasions. This is not the case on Rosh Hodesh.
Furthermore, on Shabbat and Yom Tob, if one forgot to recite "Reseh" or "Ya’ale Ve’yabo" and he realized his mistake after reciting "Boneh Yerushalayim" but before beginning the next Beracha, he inserts a special Beracha which is printed in many Siddurim ("Baruch Ata Hashem…Asher Natan…"). On Rosh Hodesh, if one forgets to recite "Ya’ale Ve’yabo" and remembers just before beginning the next Beracha, he should recite the Beracha of "Asher Natan" but without the phrase "Hashem Elokenu Melech Ha’olam" (due to the Halachic uncertainty involved). This is the ruling of Hacham Ovadia Yosef.
The Gemara comments that money spent to celebrate Rosh Hodesh (like the money spent in honor of Shabbat and Yom Tob) is not included in the amount of money G-d allocates for a person on Rosh Hashanah, and thus it will be returned to him. There is an expression, "Mi’Tishri at Tishri Hutz Mi’Tishri," which means that G-d allocates our income on Rosh Hashanah (the beginning of the month of Tishri) for the coming year, until the next Rosh Hashanah, but this sum does not include our expenses for "Tishri" – Talmud Torah (Torah learning), Shabbat, Rosh Hodesh, and Yamim Tobim. It is thus proper to spend a little extra money to celebrate Rosh Hodesh and observe it as a day of special joy and Kedusha.
Summary: As Rosh Hodesh is regarded as a minor holiday of sorts, one should eat a special meal in honor of the day. One who forgets to recite "Ya’ale Ve’yabo" in Birkat Ha’mazon on Rosh Hodesh does not repeat Birkat Ha’mazon.