Shulchan Arukh Orach Chayim · Siman 423

English

The order for reading the Torah on Rosh Ḥodesh, with four clauses: One says the full Kaddish etc, and we bring out the Torah scroll, and four read from it — no fewer than that and no more than that, and nobody does a concluding reading from the prophets.

English

The kohen reads three verses, which are "And he said," "Command," and "And say" (Numbers 28:1-3). The levite returns to reading "And say," and then reads "The first sheep" and "A tenth of an ephah" (Numbers 28:3-5). The Israelite reads from "The regular offering" up to "And on your new moons" (Numbers 28:6-10). And the fourth reads from "And on your new moons" to the end (Numbers 28:11-15).

English

And then one says Kaddish, and Ashrei, and U-Va l-Tsiyon, but one does not say Psalm 20. And one returns the Torah scroll to its place, and they stand to pray the Musaf prayer, and the precentor does the repetition of prayer, and says "Keter" to introduce the kedusha, but when he gets to "the whole earth is full of His glory" he says "to each other they praise" as in the kedusha for shaḥarit. And after one finishes the repetition of prayer, one says Kaddish and says Psalm 104, "Bless the LORD, my soul."

English

There are those who customarily remove tefillin when they want to pray Musaf.