Backup your site BEFORE you attempt an upgrade. There is a chance that upgrading will render your site inoperable. This happens if your site includes modifications/additions that are not compatible with the updated version of Joomla. In this case, each component/module must also be upgraded. In general, the above instructions *should* work on Joomla sites that are only running Joomla.
Also... some domains may not have Fantasico installed. If this is the case, then the upgrade will have to be performed manually. (You copy the upgrade patch files over your existing) Patches of course can be found at Joomla.org