Publish an event, say ButtonClicked
ButtonClickedEventArgs class may have a property of type Button pointing to
the button clicked.

Then, in usercontrol you may do something like:

Page_Load(...)
{
   button1.Clicked += myMethod;
   button2.Clicked += myMethod;
}

void myMethod(...)
{
   if(ButtonClicked != null)
   {
       ButtonClicked(this, new ButtonClickedEventArgs((Button) sender));
   }
}

etc.