Veterans would come back to these grounds years later to mark out where they were. Even if every unit didn't do this, if enough of them did we could use After Battle Reports and other documents that typically reference the placement of one's regiment in relation to another.
In the case of Chickamauga, as in the case for all of the first 5 National Military Parks, there were plenty of veterans alive to pull from so that the Parks could have accurate placements of markers and monuments. In fact, a great deal but certainly not all of the monuments were paid for and placed by the veterans themselves.
In terms of how they could remember their semi-exact placement in the middle of furious combat in the dense woods of Chickamauga, there were and are a number of fields, slopes, hills and roads on the Chickamauga Battlefield that would be used as reference.
I was at a marker for the 38th Indiana at Chickamauga where they had engaged in combat in the early morning, sat at the Northwestern corner of Winfrey field. I had with me a book on the regiment, reading quotes from men who were in the same spot as I was, describing the same field I was in, etc., etc.