Maos Rosh Chodesh:
It used to be accustomed for children to bring money to their Melamdim on Rosh Chodesh. This money is not included in the annual budget allocated on Rosh Hashanah. Some explain this money to refer to the tuition payment for the teacher, while others write it refers to a Rosh Chodesh gift.
One is to switch his clothing in honor of Rosh Chodesh. Some are accustomed to wear elegant clothing on Rosh Chodesh which are different than his weekday clothing. It is proper to at least wear one garment that is not a weekday garment. Nevertheless, one is not to wear his regular Shabbos clothing. [Practically, it is not the Chabad custom to wear different clothing on Rosh Chodesh.]
Some are accustomed to increase in lights/candles in honor of Rosh Chodesh.
It is a Mitzvah to increase in Tzedakah to the poor on Rosh Chodesh, just as is done on Erev Shabbos and Erev Yom Tov. One who increases in Tzedaka on Rosh Chodesh receives double the amount of reward that is normally given on the other days.
Tehillim/Chumash on the night of Rosh Chodesh?
One is not to recite Tehillim or read Chumash or Navi on the night of Rosh Chodesh, from nightfall until midnight, just as is the law on every weekday night.
Learning ones Tehillim:
It is an ancient custom on every Rosh Chodesh for one to study one verse from the chapter of Tehillim that corresponds to his age, together with the commentary of Rashi. If one so chooses, he may study other commentaries as well. If the Psalm comprises fewer than twelve verses, one repeats this study in subsequent months in such a way that the verses will match the number of months in that year. If on the other hand the Psalm contains more than twelve verses, one studies several verses on each Rosh Chodesh.
Visiting one’s Rebbe:
It is a Mitzvah, but not an obligation, to visit one’s Rebbe on Rosh Chodesh and to learn from him. This is because on this day there is an extra radiance of the soul of which the student can receive from. This applies equally to men and women.
Rosh Chodesh greetings:
The Rebbe Rashab was accustomed on Rosh Chodesh to wish people a “Chodesh Tov/A good month.” He would conclude: May we place effort into actual Avoda, to feel our inner vitality and have it bring to good character traits and understanding of Chassidus.
It is most proper to have a Chassidic gathering every Rosh Chodesh. Every community and Shul should have such a gathering which should include words of Torah, the saying of Lechaim, and to bless each other with good tidings and the acceptance of good resolutions regarding Torah and Mitzvos. One is also to connect the gathering with the giving of charity which hastens the coming of the redemption.
Mitzvah of Onah:
The night of Rosh Chodesh has the same status as Friday night regarding the Mitzvah of Onah for a Talmid Chacham. This does not mean that one is obligated to be with his wife during this time [if he has already fulfilled his Onah obligations or plans to do so later on in the week], but simply that it is the preferred time to perform the Mitzvah, similar to the night of Shabbos. However some Poskim write that it is an obligation to do so.
 Tur 419; M”B 419/1; Kaf Hachaim 419/1
 See Admur Hilchos Talmud Torah 1/7
 Beis Yosef 419
 Bach 419
 Or Tzaddikim 31/2; Kaf Hachaim 419/6; Yesod Veshoresh Havoda 9
 Machazik Bracha 419/2; Kaf Hachaim ibid; Ashel Avraham Butchach Tinyana 419 in name of Siddur Arizal
The reason: As Rosh Chodesh contains an extra ray of the soul similar to Yom Tov. [Chida ibid] Alternatively, as Rosh Chodesh is also called Kodesh as is seen from the term Kiddush Hachodesh, and therefore it is proper to respect the holy day with elegant clothing as by other Holidays. [Ashel Avraham ibid]
 Kaf Hachaim ibid; See there that one is to have three sets of non-weekday clothing. One for Shabbos, one for Yom Tov and one for Chanukah, Purim and Rosh Chodesh.
 Likkut Dinei Rosh Chodesh 11/5
 Or Tzaddikim 31/2; Peri Chadash 419; Machazik Bracha 419/3; Kaf Hachaim 419/7; Siddur Rav Shabsi
 Ruach Chaim 419; Kaf Hachaim [Falagi] 34/24; Kaf Hachaim 419/8; Chemdas Yamim Rosh Chodesh
 Kaf Hachaim [Falagi] ibid
 Ben Ish Chaiy Pekudei 7
 Sefer Haminhagim p. 69 [English]; Letter of Rebbe Rayatz printed Koveitz Michtavim in Tehillim Yosef Yitzchak
 For example, a thirty-year-old studies Psalm 31
 M”A 301/7; Peri Eitz Chaim 19/3; Kaf Hachaim 419/9; See A”A and Machatzis Hashekel on M”A ibid; Noda Beyehuda Tinyana 94
 Igros Kodesh Rayatz 13/440
 Toras Menachem 1990 3/382 [printed in Shulchan Menachem 2/205]
 M”A 240/3; Beir Heiytiv 240/3; M”B 240/7
 Shaar Hatziyon 240/3; see also M”A 128/70
The reason: As based on Kabala one who copulates during the weekdays draws down lower level souls for the child, while one who copulates on Shabbos draws down higher level souls. The same applies for Rosh Chodesh and there is no need to avoid having relations on this night, even if one is particular not to have relations during the weeknights, and only does so on Shabbos. Now, just as there is no obligation to have relations on Friday night so too on Rosh Chodesh. [ibid]
 Taharas Yisrael 240 Beir Yitzchak 23