How To Get A Librarian In Minecraft

As others have noted, there is no guarantee that any specific stronghold will contain a library, although from experience it is extremely rare for a stronghold to not have a library (even if the libraries are extensively damaged by other cave systems).

As of the current PC version of Minecraft, there are many strongholds in the world: up to a maximum of 128 per world. Strongholds generate in concentric rings around the center of the map (similar to how Nether Fortresses generate in "Stripes" throughout the nether). You will find strongholds in the green bands in the image below.

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This doesn't tell you where they are, but it gives you a good idea of where to look, and once you get 25km away from 0,0, they do stop spawning, so beware of that. (And the ring with the highest concentration of Strongholds is the 13696-14976, with about 0.2 strongholds per square kilometer.)

Now, back to your original question, it is possible that the stronghold you found lacks libraries. If this is the case, your only option is to find another one somewhere else in the world.

Verifying whether a stronghold has a library or not is tricky; there is no solid answer. The only way to tell for certain--without the use of mods--is to check, and to do that you will need to search carefully. I recommend traversing the stronghold as follows:

Pick a starting point in the stronghold. Usually, you'll want to start from the point where you entered the stronghold.
Choose a direction and start walking until you encounter a fork in the stronghold. Place torches on the wall to your right as you go (I recommend redstone torches, since there are naturally generated "lighting" torches that can confuse things).
When you encounter a fork, always go right. Continue putting torches on the wall to your right.
If you encounter a dead-end, turn back until you come upon a fork with paths you haven't explored yet. Pick the next path to your right and explore it.
Eventually, you will find a library, or you will end up back at your starting point. (If at any point you wish to return to your starting point, simply follow the path where the torches are on your left. Provided you placed your torches correctly, there will only be one such path from any given spot in the explored stronghold.) This will give you a good idea whether there is a Library to be had in the stronghold.
Strongholds are often not well-connected, meaning that even if you fully explore a swath of the stronghold as described above, there may be corridors that you haven't seen, obstructed by the game's cave generation. You can dig around and hope to find more sections to the stronghold. If you find any, repeat the steps above.
If you still come up empty handed, it's time to go find another stronghold and start from scratch. I suppose that in theory, it is possible that a world can have no library-containing strongholds, but from my experience that would be exceedingly rare.