Oddly enough, much like with the modern country tone, a basic jazz guitar tone eluded me for a long time. Now, I fully admit that I don't tinker with knobs like I should. I tend to set the knobs on my amps, pedals, and guitar where I think they should be and then just leave them as opposed to tweaking knobs and listening to the results. This is probably why a basic jazz tone eluded me for so long.
For some reason, there are not a lot of resources (or at least not that many that I've found) that describe a general approach to getting a good modern country guitar sound. Of course, now that I've said that I'm sure I'll get a dozen people pointing me sites that I somehow missed. But anyway, I'd like to go over what I've learned from various readings, speaking to other guitarists, and from my own experimentation.