I am not a library person but at a certain point in my life i needed to spend quite a while in this library to work on my thesis and i have the lovelies memories of those times.
You need to have your id and pay a registration fee to get inside. Then there is a security check and the cloakroom with lockers where you have to leave your camera and any books you have on you. That's the easiest part. It's very confusing even for a Russian, let alone a foreigner! But to my surprise, the old ladies working there are quite helpful and even friendly, not typical for Moscow! But again, i am not sure they speak English.
The thing i loved about the library is that i actually felt like back in the USSR.. in a good sense! The glorious main reading hall took my breath away, i didn't expect anything of this kind. It's a time machine! Finding my way to the art department through the labyrinth of corridors was another challenge well worth it. The room has an awesome view of the Christ the Saviour Cathedral and a vast collection of books on art.
By the way, they have a decent cafeteria!