1. One recites the Hallel on Rosh Chodesh. However, one does not recite the complete Hallel. Instead, one omits certain paragraphs as delineated in the prayer books. The reason for this is that since according to the letter of the law one does not recite the Hallel on Rosh Chodesh, and it is a custom from the times of the Talmud to recite it, they decreed that it should be said in its shorter form to distinguish it from the Hallel said on the festivals. (Mishne Berurah 422)
2. The custom of reciting the Hallel is both with a quorum and by oneself. Some say that even on Rosh Chodesh we make a blessing before and after it, and this is the custom of most Ashkenazy communities. Some say, however, that one should not make the blessing (as we are saying it only as a custom) and this is the custom of the Sephardim. (ibid)
