Walkthrough
Follow the Quest Marker to the Vertibird Facility, which is located to the South-West of the Lonely Chapel. Upon entering the facility, proceed down the hallway until you enter the first room. You'll notice a sealed door to your left which you cannot interact with. Instead, continue forward into the next room and prepare for combat as the area is occupied by Gunners. Take note of the window ahead of you, as you may be able to kill some of the hostiles from the vantage point it provides.
Enter the room ahead of you, and after clearing it of Gunners, make your way down the stairs. Enter the tunnel and follow the path until you enter a cavern. Make use of the available cover as you fight the entrenched Gunners and push on, reaching the catwalk and entering the Industrial Pods ahead. You'll see the Vertibird on the platform below, and your objective will now be to clear out the remaining Gunners. Quest Markers will point to every living Gunner in the facility for your convenience.
As you finish the Gunners off, you'll want to head down the stairs and onto the Vertibird Platform. On the opposite side of the platform to you there'll be an Elevator that brings you to a viewing platform. Turn right and head down the flight of stairs and go through the door. Follow the hallway. In front of you is a small barracks, whereas if you continue to your left you will reach the door you first saw when entering the Facility. Unlock the door by using the nearby terminal. Go through the door, turn right, leave the Facility and make your way back to General Ward at the Vault to report your success.
The General will be pleased, and tell you that he and the others will travel to the Facility. He'll tell you to meet them there, completing the quest and beginning The Welcome Party.