Brotherhood of Steel
You can learn the location of this location from many people, such as the singer from Junktown. Upon entering, you'll be met by two well-armed men who will give you a quest to join: retrieve the Brotherhood ribbon from the Glow . After completing this quest, return and speak with Kebbot. He'll let you in, and you'll become a candidate.
On the first floor, head to the training hall (the nurse standing right at the entrance will explain its location) and observe the combat armored soldiers training to improve your hand-to-hand combat skills. Speak with the general, who's standing right there in his motorized armor, and ask for ammunition.
Next, go to Mike, who will give you the Brotherhood combat armor and ammo. To get the motorized armor, go down to the third floor and go to the workshop. There you will find a broken motorized armor. Talk to the man standing next to it and agree to get the missing part. Return to Mike on the first floor and try to trick him.
Tell him you were sent for the Systolic Motivator, and when he asks for permission, answer that you have it, but due to bureaucrats and technology, it didn't arrive in Mike's computer. You need to choose the longest phrase. If Mike doesn't give you the part, you can steal it from General Rhombus, from his locker on the first floor.
With the part, return to Mike, who will give you a book on mechanics, and use the "Repair" skill to repair the armor. Books can also be purchased in the Hub.
Go to the training room on the first floor and learn about the missing candidate in the Hub. You'll find the candidate in the old town, in a nearby house downstairs, guarded by militants whom you must kill. The police won't interfere. Kill the militants and break down the door, freeing the candidate. Return to the Brotherhood for your reward. There, you'll be given a choice of several items. If you complete this quest before joining the Brotherhood, the motorized armor will disappear from your choice.
Go to the library and talk to the librarian, sympathize with the fact that everything is on discs now and agree with him that books are better – and he'll give you some books. You can get a disc from Vree about the mutant experiment; she'll also give you anti-radiation pills when you ask how best to protect yourself from radiation. Ask her to teach you how to use a computer, and your science skill will increase incredibly quickly.
Visit the doctor, who will perform surgery for a fee to increase all your primary skills (except luck).
On the fourth floor, you'll find General Maxson, who will give you a quest to scout the area northwest of the Brotherhood bunker. Accept this quest and ask his assistant for a weapon to complete it. Simply reach the top left corner of the world map and locate a military base. Its destruction is one of the game's main quests. Just try to avoid super mutant patrols, as they are very well armed.
Reach the military base and return to General Maxson. Tell him about the danger of an attack. Then, you need to convince the elders of the reality of the threat, and they will send a small squad of three paladins under your command to destroy the base. But don't rush into attacking the base right away, as you're still weak. After the Glow and the Brotherhood, the Boneyard is next.
See also:
Fallout 1 Walkthrough: Armor
Fallout 1 Walkthrough: Boneyard
Fallout 1 Walkthrough: Necropolis