Read the thread title. When my units get taken over by fear they can attack and move in the same turn, but when ever I move them it ends their turn as soon as I click where I want them to go. How the heck do I do it then? I love this game, but god dam it needs a dam tutorial.

It's been a while since I've played, but I believe you have to click on the enemy you want to attack and not the space you want to move to. Also, let's say your unit can move 5 spaces per turn, and you move 4, your turn doesn't end automatically. I think that's right.
 
Each unit has a certain number of action points per turn, so moving one space takes one and attacking takes one. Let's say a unit can move five spaces per turn. They can move four and still attack. But moving the full five ends their turn. I think the spaces are colored to make it more obvious.