Watch what you do! If you didn't realize this already, you should be aware that even the slightest legal missstep will result in Jason Bourne knocking down your front door and murdering you with a newspaper and ballpoint pen.
Okay, that first bit was probably a bit exaggerated. As the above video explains, getting from point A to point B via computer network isn't really as simple as googling "Who's hacking me?" From a civilians standpoint, trying to find out who's doing what on a computer probably involves something more along the lines of observing, logging, fighting (rather frustratingly) for warrants, contacting host companies, and possibly months of rinse and repeat.
Pursuing an invader isn't really worth all that the effort, especially if your case doesn't end up being the rare Cliff Stoll case (but wouldn't it be sweet if you did catch a German spy?!). Let me rephrase that; pursuing an invader isn't really worth the effort to the individual; it's just too expensive. That being said, the internet isn't a network of individuals, it's more like a manifestation of a world wide society. It's this special place that connects everyone with everyone (and everything) in a (mostly) completely open way. And like every society in existence, every individual within that society has moral responsibility to protect their neighbor. The internet is the first chance humanity has had to evolve into a truly universal, utopian society. Let's not squander this opportunity, mmkay?