The Shulhan Aruch (O.H. 8:1) rules that when reciting the blessing over the Talit, one should do so standing up. This is learned from the Mitzvah of Sefirat HaOmer, which is done standing up, since our Sages expounded the word “Kama” (lit. “stalk”) to mean “Koma” (lit. “standing upright”), and by extension it applies to other Mitzvot.
According to the Ben Ish Hai (Od Yosef Hai, Bereshit, § 66) and the Kaf HaHaim(O.H. 8:9) the way to properly don the Talit at the time of the blessing is by wrapping it around one’s head. Once complete, one may then drape the Talitaround one’s body and proceed with the prayer, and indeed this is the common custom of the Eastern Sephardic communities.
Nevertheless, the Moroccan custom is to wrap the Talit around one’s head and body at the time of the blessing. Rabbi Moshe Attia (Me’at Mayim, vol. II, § 2) explains that the Talit has to be worn as a garment, which is worn on the body (see SA, O.H. 10:10). and therefore when one performs the Mitzvah, one must mirror how is actually worn, which is, on the head as well as on the remainder of the body. As such, he states that after reciting the blessing, one should fulfill the Mitzvah by wrapping one’s head and at least a part of one’s body with the Talit. This is the opinion of the Rabbi Ya’akov Algazi (Shalmei Tzibur, § 8) as well.
Summary: The Moroccan custom to fulfill the Mitzvah of Talit is by wrapping the Talit around one’s head and one’s body.