Start from the bottom. Focus on building up resources in the big 4 cities (Chatanooga, Nashville, Memphis, Knoxville), especially Nashville. Try to find candidates that are pro-life, maybe pro gun (because those are the issues that drive Republicans from the Democratic Party).
It'll take a while, but Tennessee will become competitive sooner than Arkansas or Alabama.
This. Until those four counties, particularly Chattanooga and Knoxville, are as reliably Democratic as Memphis and Nashville, there isn't much hope. Then one needs to hope that the suburbs starts a trend democratic in the way they do in northern states or even Virginia and to a lesser degree North Carolina. However, Southern Suburban nights tend to be much more of the mega church attending social conservatives t h a n Northern suburbanites.
Until one can build up a reasonable bass and all four of those cities, Plus show at least competitive strength in the suburbs, along with what little there exists of a real black belt, Democrats at best might get lucky Illinois governor's race in a David Vitter versus JBE type of situation.