Writing Addon to Firefox with XUL and JS

This is quite simple.

Assuming your 'page modification function' looks something like this:

function install_my_button(domWindow) {

  // insert your button here (e.g: into domWindow.document.body)

  var button = domWindow.document.createElement('BUTTON');
  button.value = 'OTHER DOMAIN';
  domWindow.document.appendChild(button);
  button.addEventListener('click', function(evt) {
    domWindow.location.href = 'http://stackoverflow.com';
  }, false, true); // yes - 4 arguments!

  // that will place the button at the bottom of the page 
  // you may wish to use some CSS to position it, or perhaps
  // find a specific container element within the page in
  // which to place it.

  // prevent multiple handling
  domWindow.__my_button_installed__ = 1; 
}

Then define a 'load' event handler which looks something like this (take note that this is where we limit this code to working on the target domain (e.g: google.com):

const Cc = Components.classes;
const Ci = Components.interfaces;
let consoleService = Cc["@mozilla.org/consoleservice;1"]
                       .getService(Ci.nsIConsoleService);
function LOG(msg) { consoleService.logStringMessage("EXTENSION: "+msg); }

let wm = Cc["@mozilla.org/appshell/window-mediator;1"]
           .getService(Ci.nsIWindowMediator);

var my_load_handler = function (evt) {
  try {
    var browserEnumerator = wm.getEnumerator("navigator:browser");
    while (browserEnumerator.hasMoreElements()) {
      var browserWin = browserEnumerator.getNext();
      var tabbrowser = browserWin.gBrowser;
      var numTabs = tabbrowser.browsers.length;
      for (var index = 0; index < numTabs; index++) {
        var currentBrowser = tabbrowser.getBrowserAtIndex(index);
        var domWindow = currentBrowser.contentWindow.wrappedJSObject;            
        // identify your target page (google.com or www.google.com)
        if (/\/\/(?:www\.)?google.com/.test(domWindow.location.href)) {
          // install the privileged method (if it's not already there!)
          if (!domWindow.hasOwnProperty('__my_button_installed__') {
            install_my_button(domWindow);
          } 
        } 

      }
    }
  } catch (e) {
    LOG(e);
  }
}

You'll need to run that for all (current & future) chromeWindow elements:

let windows = wm.getEnumerator("navigator:browser");
while (windows.hasMoreElements()) {
  let domWindow = windows.getNext().QueryInterface(Ci.nsIDOMWindow);
  WindowListener.setupBrowserUI(domWindow);
}
wm.addListener(WindowListener);

where WindowListener is defined as:

var WindowListener = {
  setupBrowserUI: function(window, xulWindow, othWindow) {
    window.gBrowser.addEventListener('load', my_load_handler, true); 
  },
  tearDownBrowserUI: function(window) { 
    window.gBrowser.removeEventListener('load', my_load_handler, true); 
  },
  onOpenWindow: function(xulWindow) {
    let domWindow = xulWindow.QueryInterface(Ci.nsIInterfaceRequestor)
                      .getInterface(Ci.nsIDOMWindow);
    domWindow.addEventListener("load", function listener() {
      domWindow.removeEventListener("load", listener, false); 
      var domDocument = domWindow.document.documentElement;
      var windowType = domDocument.getAttribute("windowtype");
      if (windowType == "navigator:browser")
        WindowListener.setupBrowserUI(domWindow);
    }, false);
  },

  onCloseWindow: function(xulWindow) { },
  onWindowTitleChange: function(xulWindow, newTitle) { }
};