The Shulhan Aruch (Orah Haim 139:11) writes that when one is called to the Torah for an Aliya, he should hold onto the Sefer Torah while reciting the Beracha (listen to audio recording for precise citation). The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Toledot (18), elaborates on the details of how precisely one should hold the Torah. He writes (listen to audio recording for precise citation) that when one is called to the Torah, he should first look at the text and see the first verse that will be read. He should then cover the writing with a cloth, such as the handkerchief attached to the Torah or his Tallit, and the text should remain covered until after the Beracha. While reciting the Beracha, one should hold onto the Torah scroll – his right hand should hold onto the right scroll, and his left hand should hold the left scroll. One should hold the Torah itself, and not the casing. As it is improper to directly touch the parchment, one should hold the Torah with a cloth, such as his Tallit. The Ben Ish Hai rules that after completing the Beracha, one should remove his left hand from the Torah but continue holding the Torah with his right hand. He should continue holding onto the Torah with his right hand throughout the reading of the Torah.
The Ben Ish Hai notes that this procedure is based upon the teachings of the Arizal (Rav Yishak Luria of Safed, 1534-1572), as written in Sha’ar Ha’kavanot.