How do you join the brotherhood of steel in fallout 1

First you need to find their HQ. One easy way is going to the Hub, you can get their map location from the arms dealer, or from one of the caravans. Once there, speak to Cabbot and ask to join, he will give you a mission to go to the Glow and retrieve an artifact from there. The guard next to him will give you a Rad-X, and it's advisable to have some other anti-radiation drugs with you. Also, take a rope.

When you get to the glow, use the rope to descend into the crater. There are six levels in all with some nice equipment (such as a suit of Combat Armour) but you can get the holodisk you need from the top level. Return this to Cabbot, and you're in.