If you want to find exactly south, then you can just put a stick level ground and trace the path of the end of the shadow in the dirt. At the point the shadow is the longest, it is pointing to true north. Note the minutes and seconds as close as possible.

Then assume a longitude on the map. It's easier to use one divisible by 15. Say 105 degrees which is where I am.

Convert minutes to seconds. Say the shadow is longest 5 minutes after the hour. So it's 300 seconds past the hour.

15*300/3600=1.25

So, I'm 1.25 degrees west of 105W or 106.25W. Now you have the longitude.

Finding the latitude can also be done if you know the date. I'll let someone else struggle through that math.