1) The common custom is that the chazan bows while reciting “Barchu” (Es Hashem Hamevorach) during davening. The congregation also bows when they respond “Baruch” (Es Hashem Hamevorach Leolam Vaed)” (Kol Bo 8, Biur Halacha 57:3)
2) The Sefer Zeh Hashulchan (3 page 34 cited by Ishei Yisroel page 160), however, writes that the custom of the Gra is not to bow. (See also Shulchan Hatahor 57:1)
3) Many Sefardim have the custom that only the chazzan bows and not the congregation. (Ohr Letzion 2:5:13)
4) A Sefardi (or one who follows the Gra) who davens in a minyan where everyone is bowing should bow as well, so as not to disconnect himself from the congregation. (Based upon the view of the Baal Hatania 109:2)
5) While bowing for Barchu one does not fully bow (like the bowingduring Shemoneh Esrei), rather, one bows his head slightly. (Aruch Hashulchan 57:1)
6) The Chazzan bows by Barchu and raises himself to stand straight when he recites the name of Hashem. Similarly, the congregation bows their head at the word Baruch and stands straight when they say the name of Hashem. (See Shulchan Hatahor 57:1 and Ishei Yisroel page 160)
7) While the chazzan recites Barchu Es Hashem Hamevorah and while the congregation responds Baruch Hashem Hamevorach Leolam Vaed the congregation should stand. (148 M.B. 18)
8) The congregation may sit when they finish reciting Baruch Hashem Hamevorach Leolam vaed and they need not stand while the chazzan responds Baruch Hashem Leolam Vaed. (Beer Moshe 1:2)
9) The custom amongst many Sefardim is that the congregation need not stand at all for Barchu. (Ohr Letzion 2:5:13)
10) The poskim debate whether one must bow towards mizrach (east) or make one may bow to any direction one is facing.
A- The Tehila Ledavid (90:1) writes (regarding bowing by Modim of Chazaras Hashatz) that one must bow towards mizrach so that everyone is bowing in the same direction. Similarly, the Komarna Rebbe in his Shulchan Hatahor (57:1) maintains that one should face mizrach during Barchu.
B- The Noda Biyehuda (Tinyana 13) proves that one may always bow (both for Modim and Barchu) to any direction one chooses.
C- Harav Shlomo Zalman Auerbach zt”l seems to differentiate between bowing by Modim of chazzaras hashatz and bowing by Barchu. He holds that since bowing by Modim during chazzaras hashatz is cited in the Gemara one should do so towards mizrach. (See Siach Halacha cited in Ishei Yisroel 264) However, for Barchu (which is not sourced in the Gemara), Rav Shlomo Zalman himself was not particular and he would bow to any direction he was facing. (See Halichos Shlomo ch. 9 note 34)