Follow the saved companion. In the room with the projector, pry the door open and go through the door. Get outside across the small window. It turns out that the yard is swarming with guards. However, this means nothing if only you outsmart them and take them all down silently. When the chopper flies away, stand still. Note that at the other side, on the wooden palisade, the area is being patrolled by a soldier. Aim your bow and shoot him to the head to take him out. For this you should receive an achievement - English Pedigree.
After you shoot down the guard on the palisade, take a few steps to the right and climb onto the roof of the shack. From here, shoot (with a headshot) the guard on the watchtower. After that enter the cabin using the thin beam that you can see on the right.
While in the cabin, shoot the soldier in the next one. Then, listlessly, walk over the rope to the rooftop of the command room. Choke the man with the welder.
Walk over to the edge of the roof and jump down onto the soldier below by pressing the Y button. Lara handles the man down and, after you press Y again, hits him with a stone.
Silently, through the door, enter the command room and choke the man standing by the computer. Use the console next to you and open the gate. Before you leave, you can break the computer with the bow or with the hatchet. This is a part of a challenge - Data Corruption.