You'll now get to an area with different paths leading to various parts of the main exhibit. It doesn't matter which part you'll visit first, but to keep things in order let's start with the Wounded Knee exhibit.
Turn left at the first junction and proceed towards a room reserved for employees only. Check the table found in this room to locate a grenade launcher and Gear #9 - Head.
Return to the previous corridor and head to the room with the main exhibit. Once you're inside this room you're going to be attacked by a group of Slate's men and one Raven will accompany them. There are medical supplies to the left and to the right of the exhibit in case you need them. Once you've won the battle return to the hall leading to other exhibits. If you didn't take the grenade launcher from the employees room then I suggest that you do this now, because you'll soon encounter a motorized patriot.
You're going to be attacked by Slate's men again in the main hall. Deal with them and then proceed to the Peking Exhibit.
Just as before, when you'll reach a junction you should start by going to the room reserved for employees. Locate two valuable items on a table - a silver tab and Gear #10 - Torso.
Notice a poster located near the table. Check the back of this poster to find a lockpick.
Continue moving towards the main exhibit where once again you'll be forced to engage Slate's people in battle. Notice that there's a sniper rifle to your left (behind the rocks) and it may help you in getting rid of enemy unites. A new Fireman will soon join the battle and he'll appear on a distant hill. Kill him and once you've won the battle make sure to examine the Fireman's remains in order to obtain a new lockpick.
On your way back to the area with different paths you should notice a lockpick hidden behind a gong.