"Annual maintenance"?! Yikes. I think the first thing you should do is check it's not already been hacked and spammed to bits!
You shouldn't need to fiddle with your database at all, but you would be very wise to take a backup of it just in case anything goes pear-shaped.
Once you've done that... download the latest version of WordPress:
http://wordpress.org/download/
Unzip it onto your hard drive.
Then FTP to your webspace. Delete the wp-admin and wp-includes folders. Delete all the wordpress files in the root directory --- except the .htaccess and wp-config.php file.
The wp-config.php contains your database information, so be extra careful not to touch that. Don't touch your wp-content folder either, as that contains images for posts and anything else you've uploaded.
Then upload the new wp-admin and wp-includes folders and the files that go in the root directory from your freshly downloaded copy of WordPress on your hard drive.
You'll probably need to run a database upgrade script when you try and login to your dashboard.
Think that about covers it.
A much fuller guide is here:
http://codex.wordpress.org/Upgrading_WordPress