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On the main entrance guard, check his remains for a holodisc with the appropriate entrance code and another radio. For this you'll get 1500xp, but three of them will leave.
The less obvious approach is to use a radio if you have one in the courtyard area and trick the mutants into leaving the area. If it wasn't obvious before, I'll make it so now. The remaining ways, and possibly other minor quests I will leave up to you. Here is a list of the significant quests in the Military Base, each with a brief synopsis containing at least one way to solve it.
Vats Level 2: super mutants, Lieutenant, CoC members and the control room. Vats Level 1: super mutants, shielded areas and traps. Stronghold Level 2: the 2nd level of the base, the same but with more mutants. Stronghold Level 1: the 1st level of the base, with shielded areas and several super mutants. The courtyard, where you attempt to make it past the guards and inside With that approach, prey you are good at persuasion and/or sneaking. For details, I'll leave that to other walkthroughs, but suffice it to say you wear your robes most of the time, take the radio off the courtyard guard, read this walkthrough for at least some advice and it should unfold for you. It requires that you wear the purple robes you may have gotten from either the Children of the Cathedral hospital in The Hub Merchant area, or from the Cathedral itself. One thing I'd like you to keep in mind is that there is a less obvious approach to infiltrating the base, ala Splinter Cell and other stealth games. Yet, by now you've got the most powerful weapons and armor (if you've followed the walkthrough) and are definitely ready for a base assault. Since the Master and the Cathedral is perhaps a more dramatic ending, I'll leave that for last, though it isn't any more difficult than the Base, and actually can be quite a bit easier depending on how you approach it. It can be done before or after the Cathedral, it makes no difference since you have two main quests really form one goal: to end the mutant threats. The Military Base is one of your final objectives of the game. When you're ready for the assault on the Military Base, keep in mind you can ask a few paladins from the Brotherhood to assist for extra (hehe) support.