To bless the new moon at the proper time is akin to greeting the Divine Presence (Shechinah)...
ברוך אתה יי, אלהינו מלך העולם, אשר במאמרו ברא שחקים וברוח פיו כל צבאם, חק וזמן נתן להם שלא ישנו את תפקידם, ששים ושמחים לעשות רצון קונם, פועל אמת, שפעלתו אמת, וללבנה אמר שתתחדש, עטרת תפארת לעמוסי בטן, שהם עתידים להתחדש כמותה, ולפאר ליוצרם על שם כבוד מלכותו. ברוך אתה יי, מחדש חדשים:
The Blessing for Kiddush Levanah
Baruch Atah Adonai, Eloheynu Melech ha-Olam, asher b'ma'ah'ma'ro barah shechakim, uv'ruach piv kol tzeva'am, chok u'zman natan la'hem sh'lo yeshanu et tafkidam, sasim u'smechim l'asot retzon konam, poel emet, sh'pe'ulato emet, v'lalvana amar she'titchadesh, ateret tiferet la'amusei baten, sh'hem atidim l'hitchadesh k'motah, ul'faer l'yotzram al shem kavod malchuto.
Baruch Atah Adonai, meh'chadesh chodeshim:
Blessed are You, Lord our God, King of the universe, who with His utterance created the heavens, and with the breath of His mouth all their host. He gave them a set law and time, so that they should not alter their task. They are glad and rejoice to carry out the will of their Creator, the Doer of truth whose work is truth. And He directed the moon to renew itself as a crown of glory to those who are born [by Him] from birth, who likewise are destined to be renewed and to glorify their Creator for the name of the glory of His kingdom. Blessed are You, Lord, who renews the months.
B. Talmud Sanhedrin 42a
TANNA: It was taught in the academy of Rabbi Yishmael: Even if Israel merited no other privilege than to greet their Father in heaven once a month, it would be sufficient for them. Abbaye said, "Therefore we must recite it standing."
ADDED TEXT: Who is this coming up from the wilderness, cleaving to her Beloved? [Shir HaShirim 8:5] May it be Your will, Lord my God and God of my fathers, to fill the defect of the moon, so that there be no diminution in it, and may the light of the moon be as the light of the sun, as the light of the Seven Days of Creation, as it was before it was diminished, as it is said: And God made the two great luminaries. [Bereshit 1:16] May there be fulfilled in us the Scriptural verse which states: They will seek the Lord their God and David their king. [Hosea 3:5] Amen.
MISHNAH. R. Gamliel used to have a diagram of phases of the moon on a tablet on the shelf of his upper chamber, and he used to show them to the unlearned and say, "did it look like this or like this?"
(ד) לֹֽ֣א תַֽעֲשֶׂ֨ה־לְךָ֥֣ פֶ֣֙סֶל֙ ׀ וְכָל־תְּמוּנָ֡֔ה אֲשֶׁ֤֣ר בַּשָּׁמַ֣֙יִם֙ ׀ מִמַּ֡֔עַל וַֽאֲשֶׁ֥ר֩ בָּאָ֖֨רֶץ מִתַָּ֑֜חַת וַאֲשֶׁ֥֣ר בַּמַּ֖֣יִם ׀ מִתַּ֥֣חַת לָאָֽ֗רֶץ (ה) לֹֽא־תִשְׁתַּחְוֶ֥֣ה לָהֶ֖ם֮ וְלֹ֣א תָעָבְדֵ֑ם֒ כִּ֣י אָֽנֹכִ֞י יְהוָ֤ה אֱלֹהֶ֙יךָ֙ אֵ֣ל קַנָּ֔א פֹּ֠קֵד עֲוֺ֨ן אָבֹ֧ת עַל־בָּנִ֛ים עַל־שִׁלֵּשִׁ֥ים וְעַל־רִבֵּעִ֖ים לְשֹׂנְאָֽ֑י׃
(4) You shall not make for yourself a sculptured image, or any likeness of what is in the heavens above, or on the earth below, or in the waters under the earth. (5) You shall not bow down to them or serve them. For I the LORD your God am an impassioned God, visiting the guilt of the parents upon the children, upon the third and upon the fourth generations of those who reject Me...