There is a requirement to recite Hallel on Rosh Hodesh. Rabbi Avigdor Miller (New York, 1908-2001) explained the concept of Hallel on Rosh Hodesh as an expression of gratitude to Hashem for all He has done for us over the previous month, for giving us life, health, sustenance, joy from our children, and so on. It is also an opportunity to thank the Almighty in the advance for all He will do for us during the coming month. It is appropriate to have these thoughts in mind while reciting Hallel on Rosh Hodesh.
Rav Haim Palachi (Turkey, 1788-1869) writes that one must ensure to recite Hallel on Rosh Hodesh slowly and patiently. He emphasizes that this recitation is of profound significance according to the teachings of Kabbalah, and it cannot have its desired effect if it is recited rapidly and without concentration. Rav Haim Palachi notes that Hazanim should not be pressured by impatient congregants to recite Hallel rapidly on Rosh Hodesh, and should instead ensure to recite it with the care, patience and attention that it deserves. He notes that on Rosh Hodesh we in any event recite Hallel "Be’dilug" (skipping certain sections of the Hallel text), and it would be wholly inappropriate to rush through the recitation and end up skipping even more of the text of Hallel.
Rav Haim Palachi further writes (in his work Kaf Ha’haim; listen to audio recording for precise citation) that one earns immense merit by hosting needy Torah scholars at his table on Rosh Hodesh. Each person should provide a meal for Torah scholars, according to his means, every Rosh Hodesh, as this will guarantee his success during the coming the month. Rav Haim Palachi goes so far as to write, "Behanuni Na Be’zot" (based on Malachi 3:10), urging his readers to "test" his guarantee, and see for themselves that feeding needy Torah scholars on Rosh Hodesh brings success and prosperity. Indeed, there are several members of our community who accepted upon themselves the practice of bringing a meal to Kollel students every month on Rosh Hodesh, and the students have the donor in mind as they eat. Sure enough, the donors enjoyed much success in their endeavors. This is therefore a most worthwhile practice to adopt.
Summary: One must ensure to recite Hallel slowly and patiently on Rosh Hodesh, and it is appropriate to have in mind to thank God for the blessings he has been granted during the previous month. It is advisable to provide meals for need Torah scholars on Rosh Hodesh, each person according to his means, and one is thereby rendered deserving of success during the coming month.
