The Shulhan Aruch (Orah Haim 270) writes that it is customary to recite the Mishnayot of "Bameh Madlikin" on Friday night, a custom that is recorded already by the Tur (Rabbenu Yaakob Ben Asher, 12269-1343). The reason for this practice is that these Mishnayot speak about the guidelines for the Shabbat candle lighting performed on Friday evening. The Shulhan Aruch writes that the Mishnayot should be recited after the recitation of "Lecha Dodi," and this is, indeed, the practice in our community. Others, however, recite "Bameh Madlikin" after Arbit, and there are also those who do not recite it at all.
"Bameh Madlikin" is not recited when Friday is Yom Tob, because one of the laws mentioned in these Mishnayot is the requirement to remind one’s family members to take Ma’aser (tithes) from the produce, which is forbidden on Yom Tob. Since this Halacha is not relevant on Yom Tob, we do not recite the Mishnayot when Friday is Yom Tob. We also do not recite "Bameh Madlikin" when Friday night is Yom Tob, because, as Maran explains in Bet Yosef, people generally make thorough preparations for Yom Tob and thus do not need a reminder to take Ma’aser. "Bameh Madlikin" is omitted during Hol Ha’mo’ed and Hanukah, as well.
The Hatam Sofer (Rabbi Moshe Sofer of Pressburg, 1762-1839), in one of his published sermons, added a Kabbalistic explanation for this custom to recite Bameh Madlikin. The Hebrew word "Mishna" has the same letters as the word "Neshama" (soul), and thus as we begin Shabbat, when we are endowed with an extra Neshama, we read Mishnayot as part of the process of accepting this extra soul.
If a Minyan is held in a house of mourning, Heaven forbid, on Friday night, "Bameh Madlikin" is recited.
Summary: It is customary to recite the Mishnayot of "Bameh Madlikin" on Friday night, but it is not recited when Friday or Friday night is Yom Tob, or during Hanukah or Hol Ha’mo’ed.
