The lunar month

Karaites determine the months by the visibility of the Moon בִּרְאִיַת הַיָרֵח Biriyat hayarekh, this means when  the new moon can be seen with the naked eye, without optical aids after sunset.
The following day after the new moon is sighting is the first day of the month. ¹)
This moment is determined by direct observation of the Moon, the moon sighting dates are determined with the help of precise astronomical methods.
The lunar month has 29 or 30 days; the months with 29 days are referred to as shortened Khaser חָסֵר, the months with 30 days are called complete Male מָלֵא.

¹) The day begins after sunset, as it is written: From one night to another, you will keep your day of rest. (3M 23:32)

The names of the months:

The first month הַחֹדֶשׁ הָרִאשׁוֹן hakhodesh harishon / אָבִיב Aviv /   Nisan (translators note - name derived from Arah Nisan) *

The second monthהַחֹדֶשׁ הַשֵּׁנִי  hakhodesh hasheni   Iyar (translators note - name derived from Arah Aru) *

The third month הַחֹדֶשׁ הַשְּׁלִישִׁי hakhodesh hashelishi   Sivan (translators note - name derived from Arah Siman) *

The fourth month הַחֹדֶשׁ הָרְבִיעִי hakhodesh harevii   Tamuz (translators note - name derived from Arah Dumuzi) *

The fifth month הַחֹדֶשׁ הַחֲמִישִׁי hakhodesh hakhamishi   Av (translators note - name derived from Arah Abu) *

The sixth month הַחֹדֶשׁ הַשִּׁשִּׁי hakhodesh hashishi   Elul (translators note - name derived from Arah Ulul) *

The seventh month הַחֹדֶשׁ הַשְּׁבִיעִי hakhodesh hashevii  Tishri (translators note - name derived from Arah Tishritum) *

The eighth month הַחֹדֶשׁ הַשְּׁמִינִי hakhodesh hashemini  Kheshvan (translators note - name derived from Arah Samna) *

The ninth month הַחֹדֶשׁ הַתְּשִׁיעִי hakhodesh hateshii  Kislev (translators note - name derived from Arah Kislimu) *

The tenth month הַחֹדֶשׁהָ עֲשִׂירִי hakhodesh haasiri  Tevet (translators note - name derived from Arah Tebetum) *

The eleventh month הַחֹדֶשׁ הָעַשְׁתֵּי עָשָׂר hakhodesh haasheti asar  Shevat (translators note - name derived from Arah Shabatu) *

The twelfth month הַחֹדֶשׁ הַשְּׁנֵים עָשָׂר hakhodesh hasheneim asar  Addar Alef  (translators note - name derived from Arah Addaru) *

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The thirteenth month הַחֹדֶשׁ הַשְּׁלוֹשָׁה עָשָׂר hakhodesh hashelosha asar  Addar Bet (translators note - derived from Arah Makarusha Addari) *

* Names of months were borrowed from the Babylonians and Chaldeans during the Babylonian exile.