Question: I see different people doing different things during duchening. Some cover themselves with a tallis, while others turn round so they aren’t facing the kohanim. What are we supposed to do?
Answer: The Gemara (Sotah 38a) writes that the kohanim must face the community while duchening (blessing them). Thus, the Shulchan Aruch (OC 128:23) writes that while the kohanim are duchening everyone else must be attentive to the beracha. They should face the kohanim rather than turn away from them, though not stare at them. This halacha is so important that R’ Moshe Feinstein (Igros Moshe OC 5:20:23) writes that one can even move in the middle of davening the amida so that they and the kohanim are facing each other.
The Gemara (Chagiga 16a) writes that one shouldn’t look at the kohanim while they were duchaning in the Beis Hamikdash. As the shechina rested upon their hands while they were pronouncing the shem hameforash (ineffable name), doing so will cause their eyes to grow dim. The Magen Avraham (OC 128:35) and Mishna Berura (128:89) write that as the kohanim no longer utter the shem hameforash, this reason not to look at the kohanim no longer applies. Rambam (Tefilla and Birchas Kohanim 14:7) and Tosafos (Chagiga 16a) write that there is another reason not to look at the kohanim as doing so can be distracting. Accordingly, the Magen Avraham and Mishna Berura write that nowadays one would be able to glance, though not stare at the kohanim. Nonetheless, the minhag is to avoid looking as a zecher (remembrance) of the duchaning in the Beis Hamikdash.
The Rema (OC 128:23) records the minhag of kohanim covering their hands with their tallis so that no one looks at them. The Mishna Berura (128:91) and Aruch Hashulchan (OC 128:36) write that this is the ideal practice. Yet, the Mishna Berura (128:92) writes that in places where kohanim would not cover their hands with their talleisim, the minhag was for the tzibbur to cover their faces instead.
Thus, R’ Moshe Feinstein (Igros Moshe OC 5:24:4) writes that nowadays when the universal minhag is for kohanim to cover their hands with their talleisim, there is no concern about seeing them. Other than married men who wear talleisim, it is impractical for everyone to cover their faces (See Mishna Berura 128:115). Therefore, it is sufficient for people to just look into their siddurim or look downwards.
In conclusion, there is a minhag not to look at the kohanim's hands during duchening, though one wouldn’t do anything wrong if they did see them. While those who wear a tallis typically cover themselves with it, there is no need for others to cover their eyes, especially as kohanim cover their hands nowadays. To avoid being distracted, it is ideal to follow in one’s siddur or to look downwards, though one must not turn away from the kohanim.