It is my turn to do my moves on the campaign map. I have been wiping out Poland, but the Teutonic Order had a stack making a nuisance of itself going in and out of my lands, so I decide to teach them a lesson. The TO stack is located at the bridge just to the east of Marienburg, and I have a cavalry stack of Mameluks and Mamluke Archers a little to the east of Poznan, and direct it to hit the TO army, moving along the road south of the river. About half way there a Polish army jumped out of the forest to the south of the road, where it was hidden, and attacked my army (and was thoroughly trounced).
Again, this happened during my movement phase on the campaign map.
Now I am new to Total War, but am a couple hundred turns into the campaign, and have moved and fought across and conquered the middle-east, Anatolia and most of Europe and all the Mediterranean islands, but have until that point, never seen the AI move on my turn (unless withdrawing from an attack or after losing a battle).
What I want to know is, how do I do this, with my armies?