Objectives: Obtain Sith launch codes
Once T3-M4 unlocks the door to the military base for you, you can replace him with another member of your party if you wish, but you may want to hold on to him for just a moment. Inside, you'll come across a Twi'lek receptionist; you may be able to persuade her not to hit the alarm, but if you can't, just threaten her and she'll back off.
Now that she's gone, you'll be able to access her terminal behind the desk. If you have T3-M4 and around 15 computer spikes, you should be able to access the command functions. Your priorities in this interface are to disable the turrets and eliminate the shields of the battle droid that waits by the elevator. If you have extra spikes, you can hack into the droids' targeting filters, causing the sweet sound of gunfire to come pouring through the walls; congratulations, you've just turned the slaves against their masters. The droid uprising will eliminate most of your Sith opposition on this level. They'll still target you, of course, but they should be weakened from the fighting, and since all the enemies on this level will be droids, you can use an ion blaster or rifle without having to worry about switching your weapons back and forth for different opponents. If you wish, you can use the terminal again to shut down all of the sentry droids, but they're easy enough to kill, and you don't want to miss out on the experience.
Begin searching the area. In a hallway to the north, you'll find the friendly Duros who helped move the bodies of the Sith troops way back when you first arrived on Taris. There's a puzzle on the wall to get him out; moving all of the panels to red will free him, while moving all of them to green will kill him. Numbering the panels from left to right, the code to release the Duros is 3, 4, 2; if you want to fry him, you'll have to figure it out yourself, you sick, sick man.
To the east of this hallway, you'll come across one of the Sith barracks, with some lone survivors of the robot rampage hiding away inside. They will use grenades before battle, so be wary of the sudden drop of health, and have Bastila queue up a couple of cures if necessary. You'll find a military base passcard in a footlocker here.
Avoiding the door to the south, for now, explore the rest of this floor. There are a couple more difficult fights, one in another section of the barracks, and one in the control center on the western end of this level. For the control center, you may wish to repair the droid in the northwestern hallway to do your dirty work for you. As for the other barracks, if you're having trouble, try sending your PC in to open the door alone by using solo mode (back button). This should goad the troopers into throwing their grenades; if you run quickly enough, you may avoid their effects. If not, at least your friends won't be affected, and you'll be able to retreat behind them and hopefully not get killed. Be sure to loot the armory to the south of the control center; there's a flamethrower attachment for T3-M4 that will be quite useful.
Once you've scoured the level, return to the southeastern room to fight off a huge battle droid that guards the elevator. Kill it, then take the lift down to the lower level of the base.