In my honest opinion, what you can do with an IP address is very limited. You can ping the shit out of it (illegal) doing what's called a DOS attack, or look up the internet provider's home country, state, and even city. And finally, you can use an IP address to report somebody to proper authorities if you suspect them of internet crime. Past that, unless you want to contact the internet provider and ask them for personal information related to the IP (which unless you are part of those proper authorities you probably won't get) there isn't much to do with them.
“Teach me how to hack!”
"What, like, with an axe?"