The first slab can be found in the lab, where you are now. Go to the control panel - you'll see a recess with S.C.A.F. sign. After activating it, the first Rosetta stone will appear.
Use kinesis to pick up this part and move it to the other side of the room, to a special cataloging system. After few moments the piece will appear in the middle of the lab, where you'll be able to reconstruct Rosetta stone after collecting all pieces.
Take the Research Facility Key provide by Ellie - you can find it in a small hole in the booth where your partner stays and leave the lab. Walk the corridor to the elevator and ride it down - in the next corridor go t its end, to the biology sector. Walls are covered with some kind of organic matter - watch out for spiting bulbs.
Clear the path and head to the end of the corridor. You'll encounter a small control room, where you can deploy gas. Unfortunately the pump is off - choose the only available door there and ride down the cargo elevator.
Upgrade Circuits 2/13 - On the wall to the right in the room with the elevator.
Text Logs 1/7 - On the table in the room with the elevator.
On your way down you might deal with Necromorphs which will appear on walls to the left and right side. After getting to the bottom you'll see a fuse box. Your task is to manipulate fuses in such way, that you'll power up both the pump and the elevator. The above screen presents the correct fuses combination.
When you power up both the pump and the elevator, you'll be attacked by few Necromorphs. This location is quite small, co remember to use stasis to slow down your opponents, which should make their elimination easier. After getting rid of the opponents go to the elevator, ride it up and go to the room, where you will deploy gas.
Wait until the door gets unlocked and follow the cleared corridor to the unlocked door on the right, more or less in the middle of the corridor. Go through the door to the next room where you'll find another Rosetta plate. Next to it you'll encounter a Necromorph with tentacles - shoot them off to quiet the monster.
Audio Logs 1/4 - On the desk to the left, after entering the room.
Alien Artifacts 1/2 - On the barrels to the left, next to X-rays.
Call the plate and use the kinesis to get it to the cataloging system, located next to the entrance door. Unfortunately during this action you'll get attacked by a horde of Necromorphs - throw away Rosetta plate for now and deal with monsters. Once everything is cleared, take the plate and place it in the proper spot.