Hi,
First, make backups because it's a big update.
Then, you'll want to export/import your Joomla users from your old website to your new website.
Then, copy the tables hikashop_ from your old website to your new website database (and make sure that the table prefix correspond to the new website's) and the files in the folders media/com_hikashop/upload and images/com_hikashop/upload if they exist from the old to the new website.
Finally, install the HikaShop install package on the new website (again ? ) and it should find all the data and all the setting.
You'll just have to reconfigure your menu items and modules and the new settings of HikaShop.
I would recommend going with HikaShop 3 on the new website. You're already doing a big update, so you should go to the latest. That way, you'll be set for some time.