You have to take the enemy missile key to the control room located in the silo complex. The most straightforward way is to go through the main complex entrance located behind the loading dock in the middle of the map. Once inside the control room you will be safe, as only the key carrier can open the control room door from outside. In order to launch the nuke you will need to let one of your teammates into the control room. He will activate the launch confirmation switch allowing you to press the launch button.
Key carrier can activate control room security by pressing the panel in the main room.
Everyone inside the control room will get killed. Have fun exploring the map, as there are many more interesting aspects to it allowing for variety of strategies. The only way to get out of the nuke blast range is to clear the base. You have to either get to the loading dock, the area above the nuke silo, or hide in the tunnel going from the resupply to the silo complex. The fastest way to the control room is through the hole in the silo door right above the nuke.