Hi Andersius,
The XML import/export tool can bring over posts, pages, comments, custom fields, terms, navigation menus, and custom posts from a site.
If you are moving the site into a fresh installation of WordPress already on another domain name, this tool provides a good way of bringing your content along with it. Please note that this tool does not move over plugins or themes like a full file/database migration would.
If you just need to change the domain name of a site on the same hosting provider you might want to check this out or ask your hosting provider for assistance:
Changing The Site URL
It's always a good idea to create a full backup of your site and download it to your PC before attempting a change like this. I hope this helps point you in the right direction.
Regards,
Keith