Can I turn a cycles material to a texture, that I can use in Unity?

Anyone know how this can be done?

So cycles baking works for exporting to unity?

Baking creates an image file just like any other image file you have, nothing at all special about them. If Unity can use image files then it can use baked images from blender.

Ok thank you.

How important is the UV map?
Can I just do the automatic one or should I spend some time on it?

if its a static model, you dont need to put much effort in the uvunwraping, but if its a dynamic one, you should unwrap it carefully. This is also valid for baking, if your model is dynamic you should’nt use full baked textures, as the shadow will be static, use only diffuse, ao and normal maps.