If any battles occurred during the turn, a battle list menu will appear. In it you can see participants and locations of the battles. To play a separate battle, click on it in the list or on the map. To play all battles, click on the 'play' button (it will start from the currently selected battle). To fast-forward through battles, click on the 'fast-forward' button. You can also filter the list with the drop-down select box.
It's also possible to play a battle by clicking on it directly on the map.
Who attacks and who defends
If you attacked and your opponent didn't, during the battle your units will always be attacking, while your opponent's units defending. If both armies attacked each other, units will take turns attacking and defending. This matters because some units are better at defending (f.e. Infantry), and other at attacking (Tanks).
Units with the best attack in your army will attack first. Units with the best defence will defend first. So, for example, it makes sense to cover your Tanks with some Infantry, in case they are attacked.
Unit's Attack and Defence represent the maximum amount of damage you deal to the opponent. Attack and defence are executed simultaneously, so you're guaranteed to deal some damage in a battle. Each unit has Hit points - so damage is applied directly to Hit points, and if the unit runs out of them, it gets destroyed. The remaining damage is then transferred to the next unit.
So, for example, 1 Tank attacks 1 Infantry and 1 Militia (all units have 7 HP each). Tank deals 6 damage (attacking), Infantry deals 4 damage (defending). Now Tank has 3 HP left and Infantry 1 HP. Tanks now deals 3 damage and Infantry also 5. Tank dies, Infantry dies, Militia takes 2 damage (carrying over from Infantry), but survives to fight another day. After the battle all HP is restored for surviving units.
If the last two units destroy each other simultaneously, the defending unit will survive.
Critical hit combines the current roll (let's say 3) with the maximum attack/defence roll (let's say 7). This produces a critical hit of 10 damage. The chance for this to occur varies depending on the unit and strategy, but normally it's around 5%.