Sanctifying the new moon, Kiddush Levanah, is a prayer recited once every month sometime during its first half - ideally at the conclusion of Shabbat. You should be able to actually see most of the moon. People go outside and bless God for "creating the Heavens… setting for them laws and times... They are joyous and glad to perform the will of their Maker." The blessing goes on to compare Israel to the moon; just as the moon constantly renews itself, so too do the Jewish people. The Talmud compares Kiddush Levanah with greeting the Shechinah, the Divine Presence.
The waxing and waning of the moon represents our history, the cycle of nature, and the sacred in our lives. We end the prayer by greeting three people , "Peace to you", translating our feeling of closeness to God and creation into closer connection with the people in our lives.