The goal here is pretty much to learn the ropes and get out of the cave. But be sure to look around a little to pick up some health berries etc.
Starting out, a cut-scene where you will be asked to repeatedly press (X) key on the gamepad to fill up the knife silhouette.
When you are up just run towards the hillside where the Axe Climb text appears. Climb the rock and the rest is pretty straight forward even though there are some nasty camera angles.
Hope this helps someone out there!