In Prometheus, how did they determine the location of LV-223 just by looking at a bunch of cave drawings and inscriptions?
Simply put, they followed the star map to the location of LV-223. Consider this (rather old) BBC article describing the discovery of a prehistoric map of the night sky discovered on the walls of the famous painted caves at Lascaux in central France.
It was found:
the map, which is thought to date back 16,500 years, shows three bright stars known today as the Summer Triangle...
A map of the Pleiades star cluster has also been found among the Lascaux frescoes.
The only reason I'm citing this article is to show that cave paintings are enough to pinpoint locations in the sky. The logic is that the map on the cave wall was detailed enough to find LV-223.
Of course there are still problems with this, such as how they were able to narrow down a portion of the night sky to a single specific location - but it seems likely these problems are irrelevant plot issues that were never intended to be seriously discussed. They found a map to a location and used their technology to work out its exact location and followed it. I think that's as far as we can read into things.