After having talked with Karliah, she will direct you toward Winterhold. She tells you that only Enthir can be trusted in these matters. Fast Travel there if possible. Otherwise, it is a bit of a trek. Once in Winterhold, head into the Frozen Hearth.
Inside the Frozen Hearth, head straight across from the door. You will find Enthir sitting at the table there. Approach and talk with him. He will recognize the language as Falmer. He will explain that Calcelmo in Markarth might have the resources you need to translate this document. Head on outside and then you need to make your way over to Markarth.
Once inside Markark (be sure to try to save the person just inside at the Jeweler's stall if this is your first visit). From there, head up the stairs just to the left and make your way to Understone Keep. This is marked on your map as soon as you arrive in Markarth. Once inside, head over to the left. You will find Calcelmo at a small work station here. Talk with him.
Calcelmo is Impossible to bribe or intimidate and very difficult to persuade. Persuade is your best chance and you need a high skill in it to have a chance at succeeding. If you helped him during Book of Love or by killing off Nimhe, he will at least grant you access to his museum. This will let you walk straight through to the Laboratory.
Otherwise you will need to steal the key from the small stone table nearby and then sneak inside the museum itself. The first room must be navigated with stealth to avoid being notice.
Head across the way from Calcelmo and you will find his Dwemer Museum. Go to the first room and hang to the right. There is a pair of guards talking in the middle of the section. While they are talking, slip by them. Continue on to the West and head up the stairs. Get to the door, pick it (Adept Level) and slip inside Calcelmo's Laboratory.
Inside the Laboratory, head over to the right. Go through the doorway to the West and sneak toward the Western side of the next room.
Watch carefully because there is a guard who patrols from the Northern corridor over to the Western door, to the South and then circles back to the North. You can either kill them or wait for them to move away. If you wait by the Southwestern pillar for them to start moving back North, you will find a pull lever. Activate it to quickly (and quietly) eliminate the guard. Loot the body to retrieve Calcelmo's Laboratory Key. After that, head over to the Western door and head through it.
Head up the stairs behind the door. Sneak up the last flight of steps. There are a few guards at the top. When you get to the top you will find a pair of guards talking. You should wait for them to start walking down the corridor and sneak through behind them. If you are an Argonian, head across from the top of the stairs and down the other ramp. Grab and drag the nearby body over to the floorplate nearby. This will deactivate the gas in the area and let you easily get to the far side of the area. There you will find a valve you can open to trigger the local traps and kill the guards.
Either way, having made it to the far end, head North and East. Use an arrow to distract the guards in this room then make for the Eastern door. Go to the North and through the opening there. You will find some more Guards and Aicantar. If you can, try to sneak through. An Invisibility potion is highly recommended. If you just want to get through though, head over to the East. You will find a valve. Interact with it to activate all the traps in that room. It will kill everyone inside.
Once the area is clear, head over to the Southern alcove just before the stairs to the East. You will find the Dwemer Puzzle Cube sitting on a shelf there. Grab it and then head through the door to the East. Head up the stairs to the South and into the next area: Calcelmo's Tower.
Inside the tower, head straight to the South. Go either left or right and climb the stairs one flight. From there, jump up onto the raised area in the Southern portion of the room. You can also go up the adjacent flight of stairs and jump onto the ledge that way.
Head back out of the room and over to the tablet you can see in front of there. Go over to it and interact with it. This will let you take a rubbing of it. Immediately take cover after that. There will be a small squad of soldiers that comes in. Drop off the platform and head up either set of stairs to the East or West. Head over to the edge and wait for the soldiers to pass by. Once they have, head out the door.
Back outside you have a few choices. You can head back through the museum, dodging all the guards again or you can jump down into the pond below (save first in case). Just judge carefully if you opt to jump. From there, just make your way back to Winterhold and the Frozen Hearth. Go down into the basement and you will find Enthir and Karliah. Talk with Enthir and Karliah as prompted. As the quest ends you will be rewarded with the Nightingale Blade from Karliah. Enthir will now be available as a Fence for stolen goods.