While reciting the first berachah over the Torah when getting an aliyah, both hands should be used to grasp the 2 wooden handles of the Sefer Torah. During the layning, the right hand should continue to hold one handle (what about a lefty? A machlokess acharonim [of course]! R’ Chaim Kanievsky seems to hold that the lefty should use the right hand also). Both hands (and both handles) should again be used when making the final berachah.
Shabbos Bulletin Parshas Yisro 5779
About the Author: Lev Seltzer
Lev Seltzer has been a member of Beis Tefillah from just a short time after its founding. He currently manages the BTYA.org website, and can be found every morning in the BTYA "Vasikin Room" where he is the gabbai of the minyon.