Well, for starters, there are two guitar players. Charley McCoy, Joe McCoy's brother, more known for his mandolin playing, is backing Tommy on several of his earliest recordings.
I've never worked the two parts out, but if you are gonna give it a try you might be interested in this video on youtube:
This is Houston Stackhouse, whom I believe knew Tommy Johnson, and he is doing a pretty straight cover of the song, with another guitarist. You should be able to get some ideas.
Don't be daunted. Figuring out two guitar parts is not necessarily as tough as it might seem. And this song isn't that complex.
: Beautiful vocalist, subtle guitar style,
: tragic content.
: does anyone have a handle on 'Cool drink of
: water blues'? Is there a pick or a simple
: way in?