Hi,
You can go in your phpmyadmin and export the hikashop_ tables there.
Then, you can import the file in your new database with phpmyadmin.
Then, when you install HikaShop on your new website it should find all the data.
You'll also want to copy the files in the folder media/com_hikashop/upload (or whatever is the folder path where your images are uploaded) from your old website to your new website via FTP.
The best is to regularly backup your whole website.
On our end for example, we have custom scripts on our servers to backup things regularly. The database is backed up every few hours, the files are backed up once a days, etc. And they are backed up on different servers so that even if the server is not recoverable, we still have the backup and can rapidly put back a website online.
As a first backup tool, you can look at the Joomla extension Akeeba Backup.