General Robert E. Lee has been quoted as saying "if I make it to the blue rodge mountains, I could hold out for 20 years". So, why didn't he? A guerrilla war would have been much easier to fight then the conventional war he did indeed fight. So, what gives? What could this have looked like?
I don't know what year he said that in, but the main reason the South didn't do that was because it would cost them legitimacy in the eyes of the world. And by the time that legitimacy could never be won, it was too late and would do nothing for the South but make things go even worse.
I'd imagine a guerilla war would look like an extended version of the low-level guerilla fighting in places like East Tennessee.
However, there were areas without strong Unionist support (like Appalachia) which could have been used for guerilla fighting. Take a drive through the South and you can see plenty of places. Middle Tennessee, for instance, is full of hilly, forested terrain, and had a decent majority in favour of secession (not as much as West Tennessee, far more than East Tennessee). The same goes for much of Alabama north of the Gulf Coast, which in turn is full of swampy, forested terrain. Arkansas, of course, the Ozarks. Georgia, yeah, good land too. Now yes, these areas not used for plantations tended to be full of poor whites who had much more divided loyalties, but the potential is there for small-scale operations to wear down the enemy.
Of course, counter-insurgency is equally doable in these regions, and eventually the local population is gonna get sick of things because the war is blatantly lost at that point.