I've been solving a couple of these.. I made it through all the easy levels without ever having to divide the whole grid into specific regions (at least not consciously); I've seen that this is a common technique, but it confuses me even more when trying to apply. 
Now I'm trying the hard levels but I am big time stuck. Can someone solve this for me step by step and explain how I need to wire my brain in order to solve this??

I will be forever grateful.