The Medium gameplay focuses heavily on light puzzle-solving (and oddly satisfying flesh cutting). Throughout the game, you'll have to use Marianne's abilities to see the material and spirit worlds simultaneously to uncover what is really going on in the Niwa Hotel and how what happened there is connected to her past.
In your journey to uncover Marianne's true story, you'll encounter a water pump puzzle (in the water pump facility) after unlocking the bunker's door that is located in the red house basement. There's a monster on the loose, and he definitely wants to use you in some way, so here's the puzzle's solution so you can continue with your journey in no time.
How To Solve The Water Pump Puzzle
You'll enter this area because Marianne is running away from The Maw. And while the exit is just in front of you, the chamber is completely underwater, so you have to find a way to drain the water to pass through.
To do that, you'll have to find the control room and interact with the control panel in order to move the water from one chamber into the other. However, before you enter the room make sure to first turn off the switch on your right so you don't get electrocuted.
Once inside, you'll see there's a map indicating how many water tanks are out there and the position of the control room. You'll notice that the exit is located in the central chamber, which of course, is the one completely floated.
There's also a control panel in that same room. By interacting with it, you can manipulate the water that's pumped into the west and east chambers. But before you can use the panel, you'll need to turn the power on and open the water tanks for each chamber.
How To Restore Power
Go to the door on your left and interact with the buttons to open it. The room where you're now is where the fuse box is; ignore it for now as you first need to find some sort of energy to power it up. Keep going through the door on the left of the room and Marianne will enter a hallway, keep walking, head downstairs, and you'll find yourself in the central area where you can see the water.
This time you're going to go to the path that's on your right. You'll be now in another hallway. When the camera switches angles, don't go up the stairs but instead take the path on your right, there you'll find a room with a spirit well in it, interact with it and head back to the room with the fuse box, then power it up.
How To Open Tank Number One
Now that the power is on, you can move the water; however, both tanks are closed off. So you'll need to open the tanks manually. At this moment, The Maw will appear again and start teasing you, but you can just get out of the room and ignore it for now.
It's time to go to the first tank, head to your left through the same door that leads to the fusion box, keep following the path until you can turn left, do that, and then head downstairs, keep following the stairs, and you'll see moths in the spirit world, use Marianne's shield and go through them. You'll eventually find a red valve; just interact with it to open the tank.
Now you have to go back the way you came, but the moths are still there, and Marianne has less power now. Don't worry, as you can just go out of your body and charge your power in the nearby spirit well. Now go upstairs and head back to the control room.
It's Time To Pump Some Water
Once you're in the control room, head over to the panel and interact with the "water pump 1" button to move the water from the central chamber into the west chamber (you'll need to touch the button twice to fill the west chamber with water fully). Once that's done, push the "water tank 1" button to fill the water tank as well. Now you can drain the water that's in the east chamber into the central chamber.
How To Open Tank Number Two
Go to the door on your right and follow the path until you can go downstairs, head all the way down, and you'll find where the valve is supposed to be; however, it's missing a part. Don't worry, as you'll find it in a locked locker not far from where the valve is.
Open the locker, get the piece, assemble the valve and interact with it to open the second tank. Now head upstairs back to the control room. Before you head back, there's a hidden spirit well you can use to charge up Marianne's power. All you need to do is have an out-of-body experience and walk towards the well that's in the location in the photo.
Pumping The Water Part Two
Now that you're back in the control room is time to move the water back to the east chamber. First, fill up half the chamber and then use that water to fill the second water tank. You'll see there's water left in the central chamber, so move it from there into the west chamber. The final water distribution should look like in the picture above.
Finally, all is left to do is to head downstairs and exit the place through the exit door in the central chamber. Doing so will complete the puzzle.