Notification of purchase by email

That's done automatically normally.
If you don't get any emails from your website (for example if you try to use the mass email feature of joomla), it means that either the email settings of the configuration are not OK. Please ask your hosting company for the proper settings.
If you do get the emails from joomla, but not from HikaShop (for example if you activate the user account activation and that you register via the checkout of HikaShop but don't get the email) that the emails settings in the hikashop configuration are not OK. Again, please ask your hosting company for the proper settings.
If you get those emails but not the email when an order is confirmed, please check that documentation:
www.hikashop.com/en/support/documentatio...or.html#notification