You can hit enter, tab, or the button in the lower right. At least with the options I have enabled, though, the game won't end the turn if there are idle units or cities, or other actions that need taking (like a champ levelup).
The button in the lower right will change its title depending on the actions that need to be done. Then, when eveyrthing -is- done, you sometimes have to hit it twice (I think it does a final check, or something).
When the button has a kind of moving highlight on it, it means you're really done. Was confusing for a while, but once I figured it out, it was handy (other Stardock games tended to end turns before I was ready for them, so this helped).
I sure appreciate you taking the time to answer my question, Thanks Roccandil.