When you go to the Buffalo Pile, there's a bunch of rooms and if you go through them you can reanimate a Buffalo Soldier. Do not kill them ("Fight") at any point or else you won't be able to complete this. You'll need some things (all of which are found in the rooms here):
Get the Buffalo Soldier Diagram so you know what it consists of. It's in the locked box, but there's a key in the robe next to the concrete slab.
Once you have that, you'll be able to grab the correct Buffalo Soldier Bones from the cabinets
You'll finally need to pull together a Beaker of Buffalo Reanimating Fluid using the machine
The combination for the potion is fairly simple, but changes from game to game (I think). That said, do not try anything random since you won't be able to try again (the last vat used will be fused shut).
Hide in the wardrobe and they'll give you clues. It will consist of some combination of Milk, Blood and Ichor. They'll tell you some that are correct clues and some that are incorrect.
Once you've got the stuff, go to the room with the slab and voila! Buffalo Buffalo Buffalo Bill rides again. You'll also get Unlimited Bones when this happens and Buffalo Buffalo Bill will now join you in combat which is awesome.
You can actually make one additional thing as long as the first one ends in Lemonade (since you don't need Lemonade for the reanimating. Some combinations that work:
Milk, Milk, Lemonade --> creates a Beaker of Fudge that gives an+23 to all (M/M/M)
Lemonade, Lemonade, Lemonde ---> Beaker of Lemonade (shocking, I know) that give +15 to all (M/M/M)
If you've already started the Pet Cemetery quest and have the list of Buffalo skeletons (the Pet Cemetery guy will give this to you if you've gone in to look to see that it is missing), you also are able to grab the Buffalo bones here to complete the Buffalo skeleton.