To get to the Enclave you must get the tanker in San Francisco up and running again. You need to help the vagrants in order to get their co-operation. Just complete the two quests I mentioned in the San Francisco Area. Then hack into the mainframe of the Hubologists, or into any computer in the Shi Temple to direct fuel to the tanker. Now go to the basement of the tanker once more and use the fob on the door there. Then install the Nav Comp parts and you are ready to go. Before you leave, you might want to leave your allies outside of the tanker. If you go alone, you won't be attacked by the enclave guards. But if you have Marcus (Pulse/Plasma Rifle), maybe Vic and Cassidy (Gauss Rifle!) and Sulik of course (HK G11E) on your team, you can attempt a frontal assault. If you plan to do that, make sure, that all your NPCs that can, wear Power Armour (Weapon Store, 2nd tray) Take some plastic explosives with you! Don't forget to take your G.E. C.K. with you. Go to the bridge and talk to the captain, then activate the tanker.

If you brought your NPCs with you, wipe out the turrets at the entrance. In general, you need to save very often, because the enclave guards are really a force to be reckoned with. Consider using a Gattling laser once you found one, because this little item quite often knocks your enemies down robbing them of a few action points. Don't bother picking up all of the useless junk your enemies carry (you can't shoot with more than one pulse rifle, can you?) but be sure not to miss important things like ammo, and if you haven't got two of the YK42b Pulse Rifles pick up another one when you get the chance, so both you and Marcus have one. Always make sure your NPCs are well supplied with healing stuff. (don't give Cassidy Super Stims (his bad heart)) You can rest whenever you want to (and the area allows it), there is no time limit.

If you came alone, just explore the area as you please, no one will interfere with you. Fight or sneak your way through the Enclave, looting the place as you go. At one point you will come to a maze of nine rooms, each of them containing only one computer console, that activates some doors. Before entering the maze, save and heal your NPCs and yourselves. In the left room a suit of Enclave Armour MK II can be found and in the room to the right another G.E.C.K. is waiting for you. Both items are guarded by several troopers. But take both of them anyway.

 Use the terminals in the order listed below:

2 ? 3? 1 ? 4 ? 5 ? 3 ? 7 ? 8 ? 9 ? leave to the south
 

Go down the stairs and make your way to the lowest level of the Enclave. On your way down you will run across the President of the Enclave. He will tell you lots of interesting things about the Vaults, like why they were build in the first place. Feel free to kill this ass when your finished listening to him. Make sure to take his passkey with you.

On the lowest level you will find the mainframe, and, in the lower left corner a scientist (and of course lots of troopers everywhere). You need to shut down the reactor so that the Enclave base will be wiped clean of the face of Earth (aw, come on, you didn't think one more tiny nuclear explosion was going to make things worse, did you?) There are two ways to do this: Either blow up the mainframe, or (as I always did) convince the science guy to shut down the reactor for you. When you've done that, get the heck outta there!!!

On the First Floor, right next to the Exit, Frank Horrigan is waiting for you. If you want to, you can make this fight a lot easier for you.
First, when entering the room, you'll notice some troopers that don't attack you. (if you're alone anyway) If you are eloquent enough, you can convince them to battle Horrigan with you.
Second, the presidential passkey allows you to shut down, or recalibrate the defensive systems in the entry hall. Just move along the wall stealthily and use the terminal.
While fighting Frank Horrigan, always aim for his weapon bearing hand. If you manage to cripple his plasma gun, hell be at severe disadvantage. If you have allies in the fight, consider using the Gattling Laser, two shots will usually force him to his knees, costing him AP in the next round.

If you are alone, you will have a more difficult time trying to kill him, but you get the chance to hear his final words. After the final shot (you'll notice that one I'm sure) end combat (no need to let him die to quickly) and talk to the dying cyborg. (What the heck does Semper Fi mean anyway?)