Rosh Chodesh is among the holidays on which it is appropriate to rejoice. However, there is no explicit commandment to rejoice on Rosh Chodesh by partaking in festive meals. While it is meritorious to have special meals on the day, one is not obligated to do so (Shulchan Aruch, Orach Chaim 419:1).
Nevertheless, it is forbidden to grieve on Rosh Chodesh, and one may not fast on the day (ibid. 418:1). Anyone who refrains from eating on Rosh Chodesh, even for a short period of time, with intention to fast, commits a transgression. But if, by chance, one did not manage to eat for several hours, this is not considered a fast (Bi’ur Halachah 418, s.v. assur; Kaf HaChaim 3). According to the letter of the law, a person who ate only fruits on Rosh Chodesh is not considered as one who has fasted and transgressed a prohibition; rather, he simply failed to fulfill the mitzvah of enjoying festive meals on the day.
The main way to fulfill this mitzvah is by adding a special dish to one’s regular menu in honor of Rosh Chodesh,. even when Rosh Chodesh coincides with Shabbat(Mishna Berura 418:2, 419:1-2).
Even though one is not obligated to eat bread at a Rosh Chodesh meal, it is a mitzvah to do so (Sha’ar HaTziyun 419:1).
It is proper to set the table respectfully for a Rosh Chodesh meal. Some are meticulous about eating meat and drinking wine to celebrate the occasion.
When Rosh Chodesh lasts two days, there is a mitzvah to prepare festive meals on both days. This mitzvah is fulfilled mainly during the day, but some say that there is a mitzvah to eat larger meals at night, as well.
One is forbidden to do things on Rosh Chodesh that evoke sorrow. Therefore, eulogies are forbidden on Rosh Chodesh. If, however, the deceased was a Torah scholar, we eulogize him, but only if the body is present (Shulchan Aruch, Orach Chaim 420:1, with Mishna Berura; Yoreh De’ah 401:5).
Similarly, the custom is not to visit cemeteries on Rosh Chodesh. Therefore, if the anniversary of death (yahrtzeit) or the end of sheloshim (the first thirty days after death) coincides with Rosh Chodesh, the friends and relatives of the deceased should visit the grave on the day before Rosh Chodesh. And if that is impossible, they should go after Rosh Chodesh. One is permitted to visit graves of righteous Tzaddikim on Rosh Chodesh because this does not evoke sorrow.
A bride and groom who follow the custom of fasting on their wedding day (Ashkenazim and some Sefardim) should not fast if their wedding takes place on Rosh Chodesh(Shulchan Aruch 573:1).
Rashi states in Ta’anit (15b), “Even though it is called a mo’ed (appointed festival), [the Torah] does not call it a day of feasting and joy.” The Rosh (Berachot 7:23) concurs, stating that we do not insert the word simchah (joy) into the corrective blessing for Grace After Meals on Rosh Chodesh (see below note 14). In contrast, the author of Sefer Yirei’im (227) writes, “One is obligated to rejoice on Rosh Chodesh,” albeit one is not obligated to eat bread at the meal, because one can satisfy the requirement of joy by eating meat and drinking wine. The final halachah remains as stated above.
The Rambam holds that the prohibition of fasting on Rosh Chodesh is derived from the Torah, while the Beit Yosef (418) maintains that it is a Rabbinic decree. Pious individuals have a custom to fast on two specific Rosh Chodesh days –the first of Nisan, when Aharon’s sons were stricken, and the first of Av, when Aharon died (Shulchan Aruch 580:2). The Rama comments (ibid. 580:1) that one should not fast an entire Rosh Chodesh, rather he should eat before the stars emerge. A regular person should not accept upon himself to fast on these days of Rosh Chodesh. See Sefer Rosh Chodesh 14:13-14.
 The custom to embellish the mitzvah by setting the table respectfully is cited in Ben Ish Chai (Shanah bet, VaYikra 10) and Kaf HaChaim (419:5). Eating meat and drinking wine is also an embellishment in honor of Rosh Chodesh. According to Sefer Yirei’im, however, it is an actual mitzvah, as mentioned in the previous note. This is why most Sefardic Jews refrain from eating meat and drinking wine only from the second day of the month of Av, in order to uphold the honor of Rosh Chodesh. The Ashkenazi custom is to refrain from meat and wine on Rosh Chodesh Av, as well (see below 8:13). Also see Sefer Rosh Chodesh, ch. 12.
The Mishna Berura (419:2) writes that there is no need to have a festive meal on Rosh Chodesh night, but the Rama of Panow (79), and the Eshel Avraham of Buchach, maintain that there is a mitzvah to do so.
 According to the Rama (573:1) and the Mishna Berura (ibid. 9), they should fast on Rosh Chodesh Nisan, because the pious have a custom to fast on that day. The Pri Megadim maintains that one who does not usually fast on Rosh Chodesh Nisan should not do so on his or her wedding day. See Sefer Rosh Chodesh 14:19. In footnote 39 (ibid.), the author discusses the case of a wedding that takes place on the [first] night of Rosh Chodesh [when the bride and groom surely fast during the day prior to the wedding]. He explains that according to the Aruch HaShulchan (Even HaEzer 61:21), who holds that brides and grooms fast in order to ensure that they are not drunk at their wedding, they should continue fasting until after the chuppah, even though this will mean that they are entering Rosh Chodesh in an afflicted state. The Kitzur Shulchan Aruch (146:1), on the other hand, maintains that brides and grooms always fast only until nightfall, because the purpose of the fast is to procure atonement.
For more on visiting graves, see Yalkut Yosef 418:6-7, P’nei Baruch 37:10, and Sefer Rosh Chodesh 14:24.