Halakhah הֲלָכָה

Benei Yisrael learn that the month in which they are freed from מִצְרַיִם (Mitzrayim, Egypt) is the first month on their calendar:

הַחֹ֧דֶשׁ הַזֶּ֛ה לָכֶ֖ם רֹ֣אשׁ חֳדָשִׁ֑ים רִאשׁ֥וֹן הוּא֙ לָכֶ֔ם לְחׇדְשֵׁ֖י הַשָּׁנָֽה׃
This month shall be for you the beginning of the months; it shall be the first of the months of the year for you.
Our rabbis consider this pasuk the source of the mitzvot surrounding Rosh Hodesh, the new month on the Jewish calendar.
In temple times, each new month would be declared in Yerushalayim. This announcement would be based on the testimony of two witnesses who had seen the emergence of a new moon.
Testifying about the new moon was extremely important, since the date of Rosh Hodesh determined which days would be celebrated as holidays. According to the Mishnah, people who saw the new moon could even break Shabbat in order to travel to Yerushalayim to testify (Rosh Hashanah 1:4).
The mitzvah of declaring a new month is known as קִדּוּשׁ הַחֹדֶשׁ (kiddush ha-hodesh).
Birkat Ha-Hodesh
After the destruction of the Beit Ha-Mikdash, there was a transition to a fixed calendar that determined when Rosh Hodesh would be, instead of relying on the testimony of witnesses. Nowadays, the Jewish calendar is completely fixed and Rosh Hodesh is always known (hundreds of years!) in advance.
There is a tefillah recited in shuls on the Shabbat before Rosh Hodesh known as בִּרְכַּת הַחֹדֶשׁ (Birkat Ha-Hodesh). During this tefillah, an announcement is made about the exact day(s) on which the new moon will appear. Many people have the custom to stand during Birkat Ha-Hodesh to remember the process of kiddush ha-hodesh, when witnesses would stand and testify (Mishnah Berurah 417:1).