Angie, you can download your site via FTP and create database dump via phpmyadmin to and do upgrade on your localhost, then you have full control. You can run PHP upgrade scripts and update database then just upload your files and database back to server. Downloading var directory is not necessary, but remember to clear the cache after upload upgraded site.
This forum topic contains some useful infromation: http://ez.no/community/forum/install_configuration/upgrade_from_older_versions_than_3_5_documentation_missing