Usually it's done like this:
1. Download all your files and sub-folders from the folder you've installed Chevereto in from your shared hosting account (usually from the public_html folder, or httpdocs folder if you use Plesk) to your PC using an FTP program like FileZilla
2. Export the database using phpMyAdmin (phpMyAdmin is usually included in your shared hosting account) and save it to your PC. There's usually no need to compres the database unless your database is extremely big.
3. Upload all the files to your new VPS with Filezilla
4. Create a new database (and database user + password) in your VPS.
5. Import the database (*. sql) file using phpMyAdmin. If you run into trouble read
this excellent tutorial.
6. Edit the includes/config.php file with a text editor (Notepad++ is a good one) and fill the new database-data from your new database
7. Upload the updated includes/config.php file with FileZilla, overwriting the old one.
You might need to change folder permissions (chmod with FileZilla, right click). Set the image folder to 777 to get your new site to work.
Good Luck! It's not that difficult, I also went from shared to VPS and have moved several sites, without too much trouble.