The Shulhan Aruch (Orah Haim 139:4; Rules that a person who is called to the Torah for an Aliya recites the Beracha, Asher Bahar Banu before the Torah reading, and the Beracha, Asher Natan Lanu Torato Torat Emet after the reading. Before reciting the first Beracha, he should open the Torah scroll and look at the Pasuk where the reading is to begin, and only then recite the Beracha. Our practice is to keep the Sefer Torah open during the recitation of this Beracha. After the reading, the Sefer Torah is closed and the Beracha, Asher Natan Lanu Torato is recited.
The Hesed Laalafim (Rav Eliezer Papo, 1786-1827) writes that one should not look at the text of the Sefer Torah while reciting the Beracha, as people might then think that the words of the Beracha are written in the Torah. Different solutions have been proposed to avoid this problem. The Arizal (Rav Yishak Luria of Safed, 1534-1572) maintained that one should place the Mitpahat (cloth) over the text of the Torah while reciting the Beracha, to make it clear that he is not reading from the Torah. The Hesed Laalafim writes that one should move his head up and down while reciting the Beracha to demonstrate that he is not reading the words.
Later (139:8), the Shulhan Aruch writes that a person receiving an Aliya recites the Beracha, Asher Bahar Banu even if he had just recited Birkot HaTorah. We recite Birkot HaTorah as part of the morning Berachot, and the second of the two Berachot which we recite is Asher Bahar Banu the very same Beracha recited before the reading when one receives an Aliya. The Shulhan Aruch notes that the recitation of this Beracha over the synagogue Torah reading is separate and distinct from the recitation of this Beracha as part of the morning blessings, as it was instituted to give honor to the Torah scroll. Therefore, even if one is called for an Aliya immediately after reciting Birkot HaTorah, he nevertheless repeats the Beracha before the Torah reading.
In the opposite case, where one was called to the Torah for an Aliya before reciting Birkot HaTorah, he of course recites the Beracha before the Torah reading, and this recitation fulfills his obligation of Birkot HaTorah. This is similar to the case of one who forgot to recite Birkot HaTorah in the morning and remembered after Shaharit. He does not have to then recite Birkot HaTorah, because he fulfilled his obligation through the recitation of Ahabat Olam before Shema. This is the ruling of the Shulhan Aruch (139:9).
It should be noted that in the case where one was called for an Aliya before reciting Birkot HaTorah, he must recite the other Beracha Al Dibreh Torah after his Aliya. The sequence of the two Birkot HaTorah is not indispensable, and thus despite the fact that he first recited, Asher Bahar Banu, which is usually recited second, he may then recite the other Beracha, Al Dibreh Torah.
The Shulhan Aruch (139:10) observes that in the Beracha recited after the Torah reading Asher Natan Lanu we thank Hashem for two things: for Torato Torat Emet (His Torah, a true Torah), and for the fact that Hayeh Olam Nata Betochenu (He implanted eternal life within us). These two phrases, the Shulhan Aruch explains, refer, respectively, to the Torah Shebichtab (Written Torah) and the Torah Shebeal Peh (Oral Torah). The first phrase speaks of Torato Hashems Torah, which He wrote, whereas the second speaks of the Torah which is Betochenu within us, as the Torah scholars are given the authority to interpret the Torah, thus referring to the Torah Shebeal Peh.
Summary: One who receives an Aliya should open the Torah and look at the Pasuk from where the Aliya will begin, before reciting the Beracha. The Torah should remain open as he recites the Beracha, and he should either cover the text or move his head in a way that makes it clear that he is not reading the Beracha from the Torah. One who receives an Aliya recites this first Beracha Asher Bahar Banu even if he had just recited this Beracha as part of Birkot HaTorah. If one receives an Aliya before reciting Birkot HaTorah, then afterwards he recites only the Beracha of Al Dibreh Torah.