The section of the prayer preceding the blessings of Keriat Shema is known as Pesuke Dezimra, and is a collection of chapters of Tehillim and other sections from the Torah. Pesuke Dezimra is book-ended by two blessings; Baruch She’amar at the beginning and Yishtbah at the end. In the Ashkenazic community, the verses of Hodu are included in the Pesuke Dezimra while among Sepharadim, Hodu comes before Baruch She’amar. The Arizal explains the Sephardic custom by saying that whereas Pesuke Dezimra contains discrete chapters of Tehillim, Hodu and the verses following it are a collection of verses from different parts of the Tanach, and thus are not to be included.
Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 5, § 1) writes that if a Sephardic person is called up to be Shaliah Tzibbur at an Ashkenazic synagogue, he may recite Hodu after Baruch She’amar because even this custom has Kabbalistic sources. Furthermore, if one forgot to recite Hodu and started Baruch She’amar, one may recite Hodu within Pesuke Dezimra.
At the end of Hodu, the verse “Hodu L’Hashem Ki Tov Ki Le’olam Hasdo” is recited. Even though the Ben Ish Hai (Od Yosef Hai, Parashat Miketz, § 13) says that this verse should not be repeated, the Siddurim Tefilat HaHodesh and Bet Oved both have this verse written twice, and this is the Moroccan custom.
After Hodu and before Baruch She’amar, Mizmor 67 (“Lamnatze’ah Binginot Mizmor Shir”) is recited and should preferably be read in the shape of a Menorah. If one does not have access to this format, one should imagine the shape of a Menorah, and it is brought down that one who recites it in this manner will be protected throughout that day. On Shabbat and Yom Tov, this chapter is replaced by Mizmor 19 (“Lamnatze’ah Mizmor Ledavid”). The Kaf HaHaim (K.H., O.H. 50) writes that the custom of the Bet El community to recite Mizmor 19 even on Hol HaMo’ed, and the Ben Ish Hai (Parashat Vayigash, § 4) says that this is logical since Hol Hamo’ed has attributes of Yom Tov. This is also the Moroccan custom.
Summary: Hodu is recited before Baruch She’amar, but may recited after if one forgot to recite it or if one is serving as Shaliah Tzibur with Ashkenazim. “Hodu L’Hashem Ki Tov” is said twice at the end of Hodu. On a weekday Mizmor 67 is said before Baruch She’amar whereas on Shabbat, Yom Tov and Hol Hamo’ed, Mizmor 19 is recited in its place.