Covering the eyes upon saying Shema:
It is customary to place one’s hand over his face [i.e. both eyes] upon reciting the first verse of Shema [until the words Baruch Sheim Kevod Malchuso Leolam Vaed]. This is done so one does not look at anything else which can disturb his concentration. [In addition, there are Kabbalistic reasons behind this covering of the eyes, and hence simply closing the eyes does not suffice.]
Eyes open or closed: The custom is to close the eyes upon saying the Shema, in addition to having them covered with one’s hand.
Which hand to use: One is to use his right hand to cover his eyes. This applies even if one is left-handed [and hence he is to use his right Tefillin wrapped hand to cover his eyes]. One’s left hand is used to hold onto the Tzitzis throughout recital of the Shema.
Using a Tallis: Some Poskim record that the custom by Shacharis is to cover one’s eyes using one’s Tallis and that so is the practical directive that should be followed. Others, however, not careful in this. [Practically, while in the earlier years some have claimed that the Rebbe was accustomed to cover his eyes using his Tallis, in the later years he no longer did so as can clearly be seen from the videos.]
Making the form of Hashem’s name using the hand: Some are accustomed to make the form of the name of God, Shakaiy, using the fingers upon placing the hand over the eyes. This is accomplished by bending the thumb to form a Yud, bending the pinky like a Daled, and the remaining fingers in the form of a Shin. [While some have claimed that the rebbe did something of this sort, practically, as can be seen in the videos, this was not his custom.]
Must one remove his glasses when placing his hand over his eyes?
Some learn that based on reasons of Kabbalah, the hand is to lie directly on top of the eyes, and hence one should remove his glasses prior to resting his hand over his eyes. However, others rule it is not necessary to remove the glasses from the eyes even according to Kabbala.
 Admur 61:5; Michaber 61:5; Brachos 13b as explains Rosh 2:3; Ravayah 46; Shaar Hakavanos Kerias Shema Derush Hei; Peri Eitz Chaim Shaar Kerias Shema 6; Siddur Arizal; Makor Chaim of Chavos Yair 61:5; Elya Raba 61:7; Kaf Hachaim 61:21
 Shaar Hakavanos Kerias Shema Derush Hei; Peri Eitz Chaim Shaar Kerias Shema 6; Elya Raba 61:7; Kaf Hachaim 61:21; Az Nidbaru 12:53
 Meaning, that one removes his hand from his eyes prior to saying these words.
Other opinions: Some Poskim rule that the eye should be covered until after the reading of this verse being that this verse also requires concentration. [Ben Ish Chaiy Vaeira 6; Shaar Hakavanos]
 For this reason, it is also customary to read the first verse out loud, in order to increase in concentration. [Admur 61:5; Michaber 61:5;] There is no prohibition against saying the verse by heart as a result of covering the eyes, as the prohibition is not applied by verses that everyone already knows by heart. [Pesach Hadevir 61:3; Kaf Hachaim 61:22]
 Siddur Arizal; Makor Chaim of Chavos Yair 61:5
 See Igeres HaKodesh 9; Od Yosef Chaiy Vaeira 1; Pesach Hadevir 61:3; Shaar Hakavanos Kerias Shema Derush Hei; Kaf Hachaim 61:21-22; Divrei Yatziv Likkutim 12
 Shaar Hakavanos Kerias Shema Derush Hei; Peri Eitz Chaim Shaar Kerias Shema 6; Elya Raba 61:7; Od Yosef Chaiy Vaeira 1; Kaf Hachaim 61:21
 Od Yosef Chaiy Vaeira 1; Beir Moshe 2:5; Orchos Rabbeinu 1:53; Dinei Iter 6:5; Leket Tziyunim Veharos on Admur ibid
 Admur 24:4 “It is a Mitzvah to hold the Tzitzis in one’s left hand, in the area corresponding to the heart, during the reading of the Shema [in Shacharis].”; Michaber 24:3; Hagahos Maimanis Tzitzis 3:80; Midrash Tehillim 35b; Shaar Hakavanos Kerias Shema Derush Hei; Peri Eitz Chaim Shaar Kerias Shema 6; Elya Raba 61:7; Kaf Hachaim 61:21
The reason: This is hinted to in the verse “Vehaya Hadevarim Haeileh Al Levavcha”. [ibid]
 Od Yosef Chaiy Vaeira 1; Minhagei Maharitz Dushinsky
 Orchos Rabbeinu 1:53
 Keser Shem Tov Gagin that so is the custom in Israel
 Piskeiy Teshuvos 61:5
 See Shaar Hakavanos Kerias Shema Derush Hei; Peri Eitz Chaim Shaar Kerias Shema 6; Elya Raba 61:7; Kaf Hachaim 61:21
 See Az Nidbaru 12:53
 Divrei Yatziv Likkutim 12