What is the requirement of covering our eyes for Shema? For example, do your eyes need to be closed? Must one cover with their hand? Does it matter which hand is used?
The Shulchan Aruch 61:5 writes: נוהגין ליתן ידיהם על פניהם בקריאת פסוק ראשון כדי שלא יסתכל בדבר אחר שמונעו מלכוין:
And the Mishna Brurah 17 explains it as: ידיהם - ר"ל יד ימין
The Rivevos Ephraim 4:44:97 brings two ideas one that one takes both hands the left in the right and covers their eyes so they cant see and be disturbed from their kavana. He also brings another way of covering which is to take ones right hand and use his five fingers make a tzura of one of Hashem's names.
In another tshuva of his in 8:564:4 he writes that it seems that one needs to only use one hand(the right one-Mishna Brurah),he also brings from the Arizal that one uses right hand to close ones eyes and the left hold two tziztos.
see the tshuvos inside for all the sources.
The sefer Ishei Yisroel perek 20:5:15-16 brings a few ideas:That the Right hand should be used,and even if one is a lefty they Right hand is still used(Orchos Rabbeinu 1:pg 53:168,and Be'er Moshe 2:1) ,If one is wearing glasses he does not need to take them off rather he can place his hand over them(Oz Nedabru 12:53).
There is a shittah which holds if one doesnt close his eyes rather he looks into the siddur while saying the first passuk because he can concentrate better than its ok (Orach Ne'eman seif 10)
The Ben Ish Chai in Parshas Vaeira 6 holds that the right hand should be used and it should not be removed until one has finished saying Baruch Shem... He writes ...ויסגור עיניו ביד ימינו בפסוק ראשון עד שישלים בשכמל"ו ויש סוד בדבר...
The basic answer: While saying this important prayer, we are not to be distracted by anything around us. Closing our eyes enhances our concentration. (O.C. 61:5)
(The Talmud relates (Berachos 13b) that it was the great Rabbi Yehuda Hanasi who began this pratice. He would often be in the middle of giving a Torah lecture when the time for Shema came. At that point, he would place his hand over his eyes and recite the Shema. )
The deeper answer: The meaning of the Shema goes way beyond the belief in only one G-d. "Hashem Echad" declares that there is no existence outside of G-d.
Our world, and everything inside of it, is created from G-d's speech at every given moment.
For a few moments each day, we close our eyes and live this reality. Our breakfast, our short, our job...behind all the packaging, it’s all essentially G-dliness.
We then open our eyes and see a very different-looking place in front of us.
But we can make it past this. For we have been reminded.
And this remains with us until evening, when it will be time for our next charge, the nightime Shema…
Although the basic requirement is to just close both eyes, for Kabalistic reasons (Arizal, Shaar Hakevonot Kriyas Shema Derush 5) one should also cover their closed eyes with their right hand (even if they are left handed).