Military Base
Mutant patrols roam the area as you approach it. Don't try to kill them all. Before entering the Military Base, make sure you have explosives in your inventory. If you requested assistance from the Brotherhood elders, you'll be met by three paladins ready to storm the base, but they won't accompany you inside. There are several ways to destroy the base.
One way is to storm it: eliminate the guards, then take the radio from one of the dead mutants and fool the guards at the base. Then, take the holodisk from another guard and read the code, which you can use on the base's entrance door. Alternatively, you can try to open it with electro-lock picks. That's it—you're inside the base.
However, there are green energy fields and a ton of mutants all around. You can easily pass through the maroon force fields, but to deal with the green ones, you need to use explosives placed right next to the emitter. Set the timer, place it in your inventory, then either right-click and select your inventory and drop the explosive, or simply enter your inventory and drop it near the emitter. There are a number of computers on the right side of the Base.
If you have a radio (you can pick it up from dead guards), try connecting it to one of the computers. With advanced science, you'll be able to do this, and now you can turn the force fields on and off using the radio. You don't have to kill all the mutants. You need to get to the third floor, neutralize the force fields using one of the methods mentioned above, and take the second elevator down to the fourth floor. Ignore the broken elevator—it leads to the vats with FEB 2. On the fourth floor, you'll have to fight the Lieutenant and his guards. The turboplasma rifle is the most effective weapon. Search the lockers and find a strange key—it's for the atomic warhead in the cathedral.
Next, go to the room with the robed men. As you approach, they will explode. Kill them all and approach the middle computer. Don't touch it, just place a pre-armed explosive underneath it, and in a few minutes, there will be an explosion, the main reactor will melt down, and the base will explode. Clear an escape route beforehand.
The second option is to enter the base peacefully; let Harry from Necropolis or the guard at the gate lead you. Then, refuse everything the Lieutenant offers you, and when he decides to attack you, enter combat mode, equip the Armor from your inventory, inject yourself with Psycho, and engage in combat. Then, all that remains is to escape the base.
After the destruction of the Cathedral and the Base, Fallout comes to an end. You will learn what happened to each of the cities as a result of your actions. Svershir will chase you out of the shelter, and here... if you have the Berserker perk or negative karma, you will kill him. Alternatively, press 'A' to enter combat mode and witness his death. When he sits in the Coordinator's chair, he is invulnerable, and at the end of the game, you will have a chance to get even with him.
See also:
Fallout 1: Junktown
Fallout 1: Brotherhood of Steel
Fallout 1: Hub Walkthrough