Here's what I do:
- Start Civ5
- Under video options, change Civ5 to not full screen
- Start FireTuner
- There are a bunch of panels in FireTuner, the one I use most is called "Game" I think. It lets you start AutoPlay for different numbers of turns. The Autoplay buttons aren't all labeled right, but the turn numbers are 1, 2, 10, 50, 100, etc or about that.
With Autoplay the AI plays all the civs and then will stop and give you control of the civ you select in the middle of the Game panel. That way you can watch how the AI plays your mod and test things.
There's a lot more to FireTuner too, but I haven't messed around with much more.