The ui system uses c# events extensively, and assumes you understand how they work. If you don't understand that, then any book/tutorial on c# will help, as it'll introduce you to those concepts, etc.
What exactly are you trying to do? I think you might be going about this the wrong way. You won't need to inherit from tk2dUIBaseItemControl in most cases. If you just want to subscribe to an event that triggers when the button is clicked, look in the tk2dUIDemoController for an example of how to hook into a button event to "do something".