Cantor Jeremiah Greenberg has produced an excellent little volume which will provide you with the history of the Rosh Chodesh, as well as how to celebrate it today. I have borrowed somewhat from this little book in preparing this article. You can order it yourself by going online to MessianicLiturgy.com, by calling him at 813-792-7252, or by writing to:
Messianic Liturgical Resources
PO Box 342083, Tampa FL 33694
The Rosh Chodesh (“New Moon”) is celebrated from the time of the physical sighting of the new crescent moon, or by the calculation of the New Moon. Most Rosh Chodesh celebrations today are based on the calculations of Hillel II. He developed the fixed Jewish calendar in about 359 CE  still used to this day. This calculated Jewish calendar was at the order of the Roman Emperor, so that the Roman authorities would not be surprised when Jews would celebrate one of the Jewish holidays.
In Genesis 1:14, we read, “And God said, ‘Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years.’ ” The word translated “seasons” is mo’edim. More properly, it should be translated, “appointed times.” The appearance of the moon or its various phases has nothing to do with seasons, but it has everything to do with the appointed times of Lev. 23:4-44.
The New Moon determines when the other Holy Days are to be observed. For instance, Yom Kippur (Day of Atonement) is observed on the 10th day of the 7th month (“Tishrei”). You have to know when the 7th month begins in order to know when Yom Kippur is to be observed. We can’t properly observe the Appointed Times without an annual calendar of months, each beginning at its own appointed time (which is the Rosh Chodesh).
It is also important to know which month begins the sacred year. For that, we have the instruction given to us in Exodus 12:2: “This month (Aviv or Nissan) shall be to you the beginning of months: it shall be the first month of the year to you.” According to the Rabbis, Adam was created on the first day of Tishrei, which remained the first month of the year as the anniversary of Creation. However, for the sacred calendar, Exodus 12:2 changed the first month to Aviv (or Nissan), in early spring.
“Also in the day of your
gladness, and in your mo’edim (appointed
times), and in the beginnings of your months, you shall blow
with the trumpets over your burnt offerings, and over the sacrifices of your
peace offerings; that they may be to you for a memorial before your God:
I am YHWH your God.” (Numbers
Just as with the Feasts of Leviticus 23, there were sacrifices to be offered in the Beit HaMikdash (Temple) for the Rosh Chodesh. We also have the following instruction, given to us by the Psalmist Asaph, in Psalm 81:
1 Sing aloud to God our strength: make a joyful noise to the God of Jacob.
2 Take a psalm, and strike the timbrel, the pleasant harp with the psaltery.
3 Blow the shofar at the new moon, in the time appointed, on our solemn feast day.
4 For this is a statute for Israel, and a
law of the God of Jacob.
Psalm 81 tells us that we can celebrate the Rosh Chodesh with singing, “joyful noise,” reading of Psalms, playing musical instruments, and sounding the shofar. Sounds good!
Numbers 28:11-15 describes all the sacrifices of animals, as well as the grain offerings and libations (offerings of wine) that are to be done for the Rosh Chodesh. Today the Beit HaMikdash (Temple) or sacrificial altar in Jerusalem are not in existence, and therefore there are no sacrifices. However, the mention of these sacrifices shows us that God considered the Rosh Chodesh to be an important part of the Sacred Calendar.
Rosh Chodesh Prayers
It is often difficult to get a minyan of ten warm bodies together to observe the Rosh Chodesh at the actual time of the Rosh Chodesh. Therefore, it is often observed on the Shabbat that occurs closest to the actual Rosh Chodesh. This is usually done with a couple simple prayers. One of the prayers from Jeremiah’s Rosh Chodesh siddur is:
u “Our God and God of our fathers, renew this month unto us for good and for blessing, for joy and gladness, for salvation and consolation, for sustenance and providence, for life and for peace, for letting go of sin and for forgiveness of iniquity. For You have chosen the righteous of Israel and all the Nations, and have established for them statutes for the new months. Blessed are You, O Lord, who sanctifies Israel, the Believers in Yeshua, and the New Moons.”
To this, Dr. John Fischer adds:
u “He who performed miracles for our fathers, and liberated them from slavery to freedom, may He quickly liberate us, and gather our exiles from the four corners of the earth, even all of Israel; and let us say, Amen.
The New Moon of (name of month) will be on (name of the day). May it be good for all Israel. May the Holy One, blessed be He, grant it to us and to all his people, the house of Israel, for life and peace, for gladness and joy, for deliverance and consolation; and let us say, Amen.” 
Both Greenberg and Fischer include the Hebrew for the above blessings. In addition, Greenberg includes the transliterated Hebrew.
One of the ancient ways of celebrating the Rosh Chodesh was with a banquet, as in 1 Samuel 20:5,18: “5And David said to Jonathan, ‘Behold, tomorrow is the New Moon, and I should not fail to sit to eat with the king. But let me go, that I may hide myself in the field until the third day at evening… Then Jonathan said to David, ‘Tomorrow is the New Moon, and you shall be missed, because your seat will be empty.” This shows that calculated New Moons were also used in Biblical times. I mention this because some will only accept the actual sighting of the new moon crescent before they will acknowledge the Rosh Chodesh. If we did it that way in Rochester, we might be a few days late, because cloudy days!
However, it wasn’t always calculated New Moons. Talmud describes how two or more witnesses would go to the authorities in Jerusalem to report the sighting of the first visible sliver of the crescent of the New Moon. Then bonfires were lit from hill to hill, or runners were sent to announce the New Moon until the whole nation was aware. However, as the Jewish people spread to many other nations, such a system of spreading the news of the Rosh Chodesh was not practical.
Apparently the New Moons were also a time to visit prophets (for teaching, or to be blessed). We read in 2 Kings 4:23: “And he said, ‘Wherefore will you go to (Elisha) today? It is neither the New Moon, nor Sabbath.”
After the return of the Jewish people from the Babylonian Captivity, the New Moon was restored as a time of freewill offerings and sacrifices, as we see in Ezra 3:5 and Nehemiah 10:32-33. However, unlike the Holy Days of Leviticus 23, I don’t see any place in Scripture in which normal work is prohibited on the Rosh Chodesh. Buying and selling on the New Moon is also permitted.
The New Moon will also be restored as a universal observance (Isaiah 66:23): “And it will be from one New Moon to another, and from one Shabbat to another, all flesh shall come to worship before Me, says YHWH.” We see this same restoration in Ezekiel 45:17; 46:1,3,6. The passages in Ezekiel also tell us that there will be animal sacrifices. This might not jive with your theology, or even my theology. In such cases, we must get our theology to agree with God’s “theology.” (I have a hunch that God doesn’t spend a lot of time studying theology.)
When we observe the Rosh Chodesh, as well as all the other Holy Days of the Bible), we are observing the same days and times that Yeshua observed. When the religious leaders (Scribes and Pharisees) did something wrong, Yeshua was quick to condemn them. Apparently they must have goten it right with the Rosh Chodesh. We never read where Yeshua criticized them for any wrongful observance or customs regarding the New Moons.
 “Common Era,” equivalent to “A.D.”
 The very first of the mo’edim is Shabbat (Lev. 23:3), the seventh day of the week. Only the sun is needed to determine this day, as it is celebrated every seven days.
 Messianic Services for the Festivals & Holy Days. Menorah Ministries; PO Box 669; Palm Harbor FL 34682. p. 241.