How would I make a GUI program that displays your Ip address with a click of a button? Please, no difficult explanations, I just started Cocoa not long ago.
[[NSHost currentHost] addresses] will get you an array of IPs. Read the documentation for NSHost.
As for displaying that in a GUI, I recommend getting Aaron Hillegass' book Cocoa Programming for Mac OS X, or any Cocoa beginners book should teach that.