Prior to the blessing on Halel, the 'Hazan says “Birshut morai verabotai” and the congregation answers “Birshut Shamayim,” because he is making the blessing on the congregation’s behalf. (1)
The custom is to recite the blessing “Likro et HaHalel” before Half-Halel and “Yehalelukha” afterward when praying with a minyan. (2)
The 'Hazan says the blessings and has in mind to exempt the congregation. Other people who are present do not say the blessings individually, rather, they respond “Barukh hu ubarukh shemo” and Amen to the 'Hazan's blessings. Some, however, write that each person in a minyan can say the blessings himself, even the second blessing “Yehalelukha.” (3) However, if one arrives at a synagogue in the middle of Halel, he may say the first blessing, but he should make an effort to finish it together with the congregation and not make his own final blessing. (4)
One who prays alone does not recite these blessings. (5)
If one finds himself in a synagogue where the custom is not to say the blessing on Halel at all, some say that he himself may say the blessings before and after. (6) If one finds himself in a synagogue where the custom is that each person says the blessings himself, he should ask one of the men there to have him in mind when reciting his blessings. (7)
The custom of the Toshabim of Fes is to follow Rambam and not say a blessing on Half-Halel at all. (8)
Hareré Kodesh:
(1) Dibré Shalom VeEmet (vol. 2, p. 38, §91) writes that the Moroccan custom, and the original custom of all Sefaradim, is to respond “Birshut Shamayim” and not just “Shamayim” as many do today. See also Sidur Tefilat Ha'Hodesh (p. 559).
(2) The Sefaradi custom has always been to say the blessing on Half-Halel, whether on Rosh 'Hodesh or 'Hol HaMo’ed Pesa'h, despite the claims of some contemporary halakhic authorities to the contrary.
There are three opinions among the Rishonim regarding saying a blessings on Half-Halel. Rabenu Tam (Tosafot, Ta’anit 28b) is of the opinion that one says the blessings no matter if one is praying with a minyan or not. Rif, as well as Ran, Ribash (§111), Magid Mishné, and Shibolé HaLeket (§174), are of the opinion that one only says the blessings when praying with a minyan. Rashi and Rambam, on the other hand, are of the opinion that one does not say a blessing at all. The difference of opinion is the following. Saying Halel on Rosh 'Hodesh is a custom, and it is a matter of dispute whether one says a blessing on a custom or not. The Sefaradi custom has always been to follow Rif, who rules to say a blessing on Half-Halel if praying with a minyan.
Maran (Shul'han ‘Arukh, 422:2) mentions the opinions of Rif and Rambam and stipulates that the custom of the Land of Israel and its surroundings is to follow Rambam, not to say a blessing on Half-Halel. Maran’s opinion is unclear, as in Bet Yosef (§422) he cites the three opinions of the Rishonim and seems to favor that of Rif. However, he does not render a clear decision and one of the fundamental principles governing the adoption of Maran’s decisions is that they are not binding when his opinion is unclear. In this specific case Rif is followed, as Sefaradim always have. Therefore, even in the Land of Israel, where Maran says that the custom is not to say a blessing on Half-Halel, Moroccan Jews must keep to their custom and say the blessing. Since they have established synagogues in the Land of Israel, they are considered a full-fledged community, and a community keeps its customs even when it moves, as the Jews did from Morocco to Israel, to Canada, to France etc. The halakha that, one who moves to another place must adopt the customs of his new home, applies only to individuals moving to a place devoid of an established community. Ribi Mordekhai Lebhar s”t personally heard this from Ribi Shalom Messas, Ribi Yosef Shalom Elyashib, and Ribi Mordekhai Eliyahu. This is also what Ribi Refael Barukh Toledano did when he moved to the Land of Israel (Or HaMa’arab, Shebat, vol. 7, p. 71).
(3) Sidur Bet ‘Obed writes that an individual (not in a minyan) can say the blessing before Half-Halel, “Likro Et HaHalel,” but not the blessing that comes after, “Yehalelukha.” However, Ribi Shalom Messas (Tebuot Shemesh, §68) says that a “mistaken student” wrote this into Sidur Bet ‘Obed, and that one can say both blessings himself when in a minyan and does not have to be included with the 'Hazan’s blessings.
(4) See Meiri (Berakhot 14a), s.v. Elu she-ameru.
(5) See the old Livorno sidurim (Bet ‘Obed, Tefilat Ha'Hodesh), who write to say the blessings only with a minyan, as well as the sidurim of Baghdad (Bet Yisrael) and Egypt (Pir'hé Misrayim). See Ribi Shalom Messas (Tebuot Shemesh, §68), Ribi Refael Barukh Toledano (Kisur Shul'han ‘Arukh, §255:10), Ribi Yosef Benaim (Noheg Be'Hokhma, p. 28), and Ribi Yis'hak 'Hazan (Ye'havé Da’at, §11). Berit Kehuna (200:5) and Sho-el VeNish-al (vol. 2, §30) attest to this being the custom of Djerba and Tunis, respectively. Ribi David ‘Obadia (Nahagu Ha’Am, Rosh 'Hodesh, §7, p. 42) writes to say the blessings, although the custom follows Rabenu Tam that they be said when praying with or without a minyan.
(6) Heard from Ribi Yosef Benaim.
(7) Heard from Ribi Yosef Shalom Elyashib. The reason is that in a synagogue where each person says the blessings himself, one must assume that the 'Hazan does not have in mind to exempt anyone else in his blessing. At the same time, a Moroccan Jew for sure cannot make the blessing himself, as his custom is to hear the blessing from the 'Hazan. Therefore, the advice in this situation is to ask one of the congregants whose custom is to say the blessing on Halel to have him in mind when saying it.
(8) See the sidur of the Toshabim of Fes, Ahabat HaKadmonim, and Noheg Be'Hokhma (p. 28).