SO lost…

Ok. It would be more impossible for me to be thoroughly confused…

I have had a wordpress blog, hosted on wordpress.com.
I wanted a domain and hosting so I could add plug-ins.
I purchased a domain and hosting and no longer understand anything.

How can I get/move the blog I already have, to the new host under the domain name? My host says I need to get a MySQL package from WordPress. ww.wp.xz.cn or WordPress.com? I try to log in to WordPress.com, but my UN & PW don;t work. Then I use the new admin ones, but they don’t work on this forum. I try searching through the forums and can’t find any relevant information, other than a post that suggests I can’t (easily) use a theme I have been using on WordPress.com over at ww.wp.xz.cn. So if I can’t use anything from WordPress, .com or .org, why do I have anything to do with it or need to log into any control panels? It doesn’t help at all that it seems that WordPress also does hosting? So when I search for answers I have NO idea if they are talking about when they are hosting or a third party.

This is ungodly frustrating…
Looking at the homepages of WordPress.com and ww.wp.xz.cn there is not something remotely simplifying or clearing up and possible confusion.

Please, please, help.