There is a Mitzva to recite a special Beracha each month over the appearance of the new moon; this blessing is called Birkat Ha'levana. The Sages afforded great importance to this Mitzva; in fact, the Zohar, as cited in Kaf Ha'chayim Sofer, writes that one who recites Birkat Ha'levana is guaranteed that he will not die an abnormal death.
Rabbi Chayim Palachi (Rabbi of Izmir, Turkey, 19th century) writes that the proper text of the passage "Baruch Yotzrich…," which is recited together with Birkat Ha'levana, is as follows: "Baruch Yotzrich, Baruch Osich, Baruch Konich, Baruch Bor'ich." This arrangement yields the acronym "Baruch Ya'akov" ("Yotzrich," "Osich," "Konich," "Bor'ich"), and is the proper text. Some Siddurim present this passage differently, but this is the correct text.
Rabbi Chayim Palachi further writes that after reciting Birkat Ha'levana one should look at his Tzitzit and examine them. He explains that the Sages likened the recitation of Birkat Ha'levana to "Kabbalat Penei Shechina" – standing in the Divine Presence and accepting upon oneself the Almighty's rule. Tzitzit very closely relates to this theme, as looking at the Tzitzit is intended to lead one to the fear of God. It is therefore proper to look at one's Tzitzit after reciting Birkat Ha'levana.
In addition, Rabbi Chayim Palachi writes that after Birkat Ha'levana one should give three coins to charity.
Finally, he writes that one should shake the bottom of his garment after reciting Birkat Ha'levana, to rid himself of the negative spiritual influences of the moon to which one is subjected when reciting this blessing. The custom is also to greet three people with the greeting of "Shalom Aleichem," and Rabbi Chayim Palachi explains the reason for this practice in accordance with the teachings of Kabbala.
Summary: The proper sequence of the passage "Baruch Yotzrich" in Birkat Ha'levana is as follows: "Baruch Yotzrich, Baruch Osich, Baruch Konich, Baruch Bor'ich." After reciting Birkat Ha'levana, one should look at his Tzitzit, donate three coins to charity, shake the bottom of his garments, and extend the greeting of "Shalom Aleichem" to three peers.