As was stated in the comment to another solution, the first place you encounter a Librarian is at the very start of "Depository." When you start this level, you can see a Librarian hunched over a dead body with its back to you. They are big lumbering creatures similar to a more upright Gorilla.
I found that even on the hardest difficulty, I was able to empty a magazine into its back from the silenced rifle given to you at the start of Black Station before it really seemed to pick up on where I was. The attacks tend to be swinging pummelling attacks, so it's easy enough to jump out of the way and attack again. It took a couple of clips of ammo from the rifle, then I switched to the automatic shotgun and fired a few more shots at point blank range to finish it off.
This is the best time to take out a Librarian if you have the ammo to do so, because once you have done it, you can simply Load Last Checkpoint to start the room again and use the eye-to-eye technique without having to waste any ammo or lose any progress.