As soon as you gain control, turn around and grab Bobby's Letter off his bed and the Kreisau HQ Map off the table.
If you haven't already done so, talk to Anya to receive instructions on your objectives, then head to the room where you can access the second level of the hideout. Try to open the door next to Tekla, who will then laugh at you and say that you need a key. Next, inspect the vent at the base of the ramp to find the spores you were looking for.
You should now be able to exit the facility from the first floor, heading into the hanger entrance where you'll find the vent with spores coming out. Inspect it to discover that you need a circular saw, which just happens to be lying on the ground close by. Try to pick it up, causing you to fall through the floor and into the sewers.
Head forward, take a left and hug the right wall. Be careful of the automatic turret up ahead. Use the Laserkraftwerk on shoot mode to disable it. Go through the broken bars and charge up before you head through the door in front of you. Go forward until you have to choose between right or left. Go right and pick up the upgrade to your Laserkraftwerk.
Head back the direction you came, taking out the automatic turret and cutting the chain on the locked gate. As soon as you go through, take out the drones with your Laserkraftwerk.
Grab the shotgun and ammo from the shelf just inside the door, then head down to the scaffolding and snag the health on top. Backtrack to where you entered the room, go up the stairs and follow along the catwalk (taking out two more drones) until you get to the far end where there's a ladder. Climb up and follow the only path you can take until you emerge in the hanger once more.
Tip: At any point during the level, head to the top floor and all the way to the far corner. You'll see a mattress on the ground with an option to interact with it. Doing so will unlock the side mission and Easter Egg - Escape from Castle Wolfenstein.
Head over to the piece of concrete and use the circular saw to cut a piece out for Anya. Head back into the hideout and into Caroline's room on the first floor. You should see a hole in the wall now. Heading through there will give you access to a back tunnel of sorts, leading you to the wall behind Max's room as well as the area of your own bedroom that you couldn't previously reach.
However you choose to get to the second floor, that's your destination. Head upstairs and see Fergus in his bedroom. He'll give you the key you need to access the archives. Go back downstairs and get the file from the archives room, delivering it to Anya along with the concrete sample to finish the level.