I try to describe a crafting process of tanning leather with nothing than a stone knife and a freshly killed animal.
This comes from my old boyscout diary and is a time-proven procedure. It would be a great addition to the survival part of the game.

As in reality almost any animal comes with everything we need to tan its pelt, in-game some things need to be implemented first.
What we need is the brain of the animal we killed as a resource and the possibility to craft a frame of wooden sticks and guts to insert the pelt to.
Another method is to stretch the pelt with some wooden sticks on the ground.

When the pelt is stretched we need to scrap away any remaining meat and fat with the stone knife.
As I skip some steps like flesh side and fleece side teatment, lets say we got a cleaned skin after step one.

Now we need to rub the cerebral matter in the skin to make it soft. This part has to be repeated depending on the thickness of the skin.
At this point we got a raw (soft) leather, but its not finally tanned yet.

To impregnate the leather it needs to be smoked. This is typically done in a teepee but in-game putting the frame, mentioned above, next to a fireplace should work.

Finally the impregnated leather needs to sluiced out in water to get rid of the aldehyde which is prone to cause itch and flush. Spending a bottle of water to it, should be enough in-game.

Smoking the leather has a nice bonus by the way. The leather gets a shade of brown depending on the intensity of the smoke and the wood used.