In order to move your Prestashop store from a webhost to another, follow these steps.
1. Backup your store from the old host. Backup the files and the sql file (the database).
2. Change the DNS so they will point to the new webhost.
3. Create the domain on the new webhost, the sql database and the username.
4. Upload the files and the sql database to the new webhost.
5. Go to config/settings.inc and change the values there. They are for the new database which should have different credentials.
6. Using a FTP software, go trough FTP to cache/class_index.php. Delete this file if the store is displaying a blank page.
That’s it.