The Sages state in a beraita in Masekhet Sofrim (14:1) that over the course of the year we publicly read all five megillot (scrolls): Shir Ha-shirim on Pesaḥ, Rut on Shavu’ot, Eikha on Tisha Be-Av, Kohelet on Sukkot, and Esther on Purim. Before beginning each reading, the berakha of “al mikra megilla” is recited. This follows the ruling of the great Ashkenazic Rishonim (Maḥzor Vitri; Hagahot Maimoniyot quoting Maharam of Rothenburg; Or Zaru’a; Shibolei Ha-leket; Maharil). However, many have expressed reservations about this ruling since, apart from Esther, we find no reference in the Gemara to reading megillot, and we certainly find nothing about reciting berakhot over them. For this reason, the great Sephardic leaders ruled not to recite a berakha before reading the megillot, and this is the universal Sephardic custom (Responsa Radbaz 6:2096; Beit Yosef 559:2).
As for Ashkenazic custom, many are of the opinion that on account of the uncertainty, it is proper not to recite a berakha over the four megillot whose reading is not mentioned in the Gemara (Rema 241:9; Taz ad loc. 6; Pri Megadim; Ḥok Ya’akov). This is the current custom of all those who pray with Nusaḥ Sepharad (including Ḥasidim), as well as some of those who pray with Nusaḥ Ashkenaz.
Others maintain that a berakha must be recited before reading a megilla (Levush; Baḥ; MA 490:9; Vilna Gaon). This is the custom of Jerusalemites whose ancestors were students of the Vilna Gaon who helped found the Old Yishuv. It is also the custom of many who are of Lithuanian descent. Those who recite a berakha make sure to read from a megilla written on parchment (based on Responsa Rema §35; MB 490:19).
Of those who recite “al mikra megilla” prior to reading the megillot, many also recite the berakha of She-heḥeyanu (Levush; Vilna Gaon). Many others question this, since She-heḥeyanu does not appear in this context in Masekhet Sofrim, and most of the Aḥaronim do not mention it. Therefore, for those with a custom to say She-heḥeyanu, it is proper to wear a new item of clothing, in which case all agree that the berakha may be recited.
Where members of various communities pray together, it is advisable for them to read from a megilla written on parchment, and for one whose custom is to recite the berakha to do so out loud. All those present can then respond “Amen,” thus fulfilling the views of all poskim. Ashkenazim read Shir Ha-shirim on Shabbat during Pesaḥ, Kohelet on Shabbat during Sukkot, and Rut on Shavu’ot. All the megillot are read prior to the Torah reading.
In contrast, Sephardim and Yemenites read Rut before Minḥa. If it was read during the Torah study of Shavu’ot night, there is no need to read it again before Minḥa (13:12 below). Most Sephardim do not have any public reading of Kohelet. Yemenites read part of it before Minḥa on Shabbat during Sukkot, and part of it on the last day of Yom Tov. They do the same with Shir Ha-shirim – reading part of it on Shabbat during Pesaḥ and part of it on the last day of Yom Tov. Sephardim and many others from various communities also have a custom to read Shir Ha-shirim on Pesaḥ after the Seder is over.