Yeah it's turn based. Similar to D&D actually - characters with high initiative get to act first. If you're playing on your own you control all party members - there's not any AI involved, unless it's an npc who just happened to be in the area or if you picked one up as part of a quest.
How good is that AI though? Let me put it this way: When the enemy AI takes control of my characters (such as with a charm spell) they use them FAR more effectively than I ever would. I've actually learned some pretty nasty combos just from watching what they did with them
One fight I distinctly remember: I'd carefully prepared the battleground pre-engagement. Had explosive traps carefully placed next to oil barrels, had my ranged characters on the high ground, melee characters near their casters. AI enemy got to go first. What do you think they did? They teleported my heaviest hitter right into the explosive trap, setting all the oil barrels on fire and killing him instantly. The enemy AI is very, very good. Pathing AI for your characters is pretty solid too. They won't, for example run through a bunch of poison to keep up with you, rather, they'll try to navigate a path around, and if that's not possible they'll stop outside the poison. I'm super impressed with it.
Oh yeah, one other thing I'd be remiss if I didn't mention: The voice acting is top notch. Lots of these rpg games can be very text heavy, but the voice acting is so well done I find myself stopping to listen to the entire conversation rather than just reading the text and skipping through like I would in many other games.
They even have voice acting for the random animals in the game world that you can talk to if you have the pet pal talent. I guess I lied - I did skip through some of the voice acting of the oxen as he was like the sloth in that pixar movie - took forever to say anything. It was very fitting for a big, slow moving ox though.