Probably the absolutely easiest recipe I've seen is...
Take a pork shoulder and put it in a crock pot.
Cover it with a bunch of bottled root beer.
Cook for 8 hours, then drain, pull apart with two forks, and eat.
There's certainly better recipes that are more involved, but for "pretty damn good with minimal effort", this one works well. A bit of hickory smoke extract makes it even better.
For a simple sauce to go with it:
Mix equal parts root beer and Heinz chili sauce
Reduce by half.
Mix in after you've drained it.