What you do - is copy all the files up (over your demo) except for the main.inc.php, config.inc.php and theme.inc.php file. Then follow the instructions in UPGRADING-DEMO.txt.
Basically it'll walk you through updating versions - but you wont' have to reconfigure anything and you won't lose your data.
If you're moving it to a different server or changing the domain name, then you may need to adjust the paths/urls found in the main.inc.php file and the config.inc.php file.
