Buiding a test site

I'm sure you could use some kind of backup tool like akeebabackup to move the whole website.

Now, if you just want to move hikashop for one website to another, you should:
1. install hikashop on the new website
2. remove all the jos_hikashop_* tables from the database on the new website via phpmyadmin
3. export all the jos_hikashop_* tables from the database of the old website via phpmyadmin
4. import the file created on the previous step on th new website phpmymadin

At that point, you will have all the data of HikaShop on the new website.

5. copy the folder templates/YOUR_TEMPLATE_ON_OLD_WESBITE/html/com_hikashop to the folder templates/YOUR_TEMPLATE_ON_NEW_WEBSITE/html/com_hikashop if it exists on the old website (it will be created when you edit views via the menu Display->Views)
6. copy the folder components/com_hikashop from the old website to the new website (the files and images you uploaded in products and categories as well as CSS customizations and emails customizations are stored there)

Here, you will have all the customized files onto the new website.

7. The big problem with that is the modules and menus. The options are stored in the hikashop tables. But the entries are in the jos_menus and jos_modules tables in the database. If you started with all the modules and menus of the new website on the old website (by having a copy of the new website for example) as you are saying or that you don't care about the modules and menus of the new website, you can just export those two tables from the old website and import them on the new website like explained on steps 2,3 and 4. And that will be all. Otherwise, you will have to recreate your modules and menus for hikashop on the new website.