Hi,
To answer your immediate question first, login (as well as registration and other basic functions) is handled by Joomla. So, there's not much that can be said here.
However, looking at your site under the link provided at the time of this writing, it appears as if it's effectively "broken". Other than the appearance indicating this, It's throwing numerous errors, and a check with the W3C Validator proves it.
This can be caused by numerous factors, such as an erratic Joomla installation, coding errors in content or customizations, the template, other extensions and plugins, etc. In fact, HikaShop seems to be one of the few things displaying and working well. So, you should investigate the other issues first, and once fixed the login (which - again - is not a HikaShop function), might work as well then.