How to modify a core theme and what is the correct way to do this? I modified the core's Bartik theme file, node.tpl.php.  I simply added 

echo "Last updated by $name on " . format_date($node-&gt;changed);


The problem is that when there is a new core update, my change will be overwritten.  Is there a way to create a module that will easily add this simple line in the node.tpl.php of Bartik's node.tpl.php theme file so that future updates will not overwrite my change?
What you want to do is create a subtheme of Bartik, and make your modifications to node.tpl.php there instead. Themes support the notion of inheritance, so this can be leveraged to tweak core themes without actually hacking core. As a rule, it is best practice not to hack core for the reasons you mentioned and a slew of others, security not the least among them.