Here's how I upgraded ViArt to test a newer version. I'm using a local server for testing with MySQL and Webmin but this should be the same procedure for remote servers/databases.
 
Firstly I backed up my existing SQL data from the existing site to a new file separate to the regular backup.
 
I downloaded the new ViArt and extracted it to a new folder/directory and changed the read/write/execute permissions to 777 for the /incudes folder. If you are uploading to a remote site by ftp don't forget to use binary transfer mode.
 
With web browser I then went to the new version folder and started the installation procedure with a new database name (I used the old one plus version number -33) but didn't populate the new database with data.
 
Using MySQL in the new database I used "Execute SQL" and used the backup file as a source to "Select an SQL commands file to execute to database .....". This populated the new ...33 database with my old existing data.
 
I then ran the new site administration screen and went to System Administration and found the existing data had populated the Site Settings. I changed the "Site URL" to the new one and clicked "Update". I then went to "System Administration > System Upgrade" and used "Upgrade" to change the version number in the database. This produced a reassuring series of errors telling be the new database fields already existed.
Note that if you use the same login admin name and password as the old site you can swop between new and old admin screens.
 
I then checked the settings in the admin section to see if they corresponded and added new settings where they were needed (such as SMTP).
 
I then copied over the old image, template and other files needed from the old to the new and changed the CMS layout source in admin.
 
A very good utility to do this is a file difference program with merge facility. Whilst this is more "long winded" than amending existing layout/css files it does mean you have an easier path to upgrading in the future as its more than likely that these will change with upgrades - as in fact they have done with 3.2 and 3.3 css files!!
 
Another hint is, before changing a file, copy it with the original filename and append "OLD" before the filetype so you can instantly see what's been changed.
 
If you are adding or changing message or language files leave the original and append changes to the end. The new definitions are parsed by php in order so replace any previous ones in the file but when you upgrade you simply copy the end of the file over to the new one.
 
There are of course issues where you have changed templates or removed parts of the site you don't want but that, as they say, is another story...

Ive now noticed that in 3.3 appending message or language file definitions throws up an error when opening admin so theres some parse checking going on. Bother it would make life easier!