In Firefox there is a menu item that displays "Page Source": View | Page Source (Ctrl+U). In Internet Explorer there is a similar function.
Before. The page source is the result of the GET request by the browser sans headers. If you want to view the updated content after scripts and so forth, you'll have to use a tool like Firebug or the Web Development toolbar.
You can use a tool like Firebug (Firefox & Chrome) to see live dom changes. Or you can make your own function to display the live dom.