This is the process I used to test the backups being made by BackWPup
Upload and extract archive to new sub-directory on server
Create new database and change database info in wp-config.php
Install fresh Wordpress using wp-admin/install.php
Activate BackWPup plugin
Go to Tools and click Restore (wp-admin/admin.php?page=backwpuptools)
http://codex.wordpress.org/Installing_WordPress#Famous_5-Minute_Install