Moving servers – Help!

I’m so stuck! I want to move my wordpress blog to a different server, and I’m having a hard time getting it right. I currently have a wordpress blog – http://www.vlnjodie.frihost.net and I want to move it to a server and upgrade to WP2.x at http://www.violinjodie.com/blog

Here are the many things that have gone wrong.
1) I have prematurly changed my domain name in my admin at the orginal blog. Now I can’t get signed back in and my blog looks weird.

2) I can move files to and from my website to my computer easily, but I have no idea how to move my database. I actually created a new database in my new server, but I’m feeling very confused. Somehow I need to get all the meat of my database (my comment, posts, catagories, etc.) to my new database. I’ve fiddled with MySql and I can’t figure out how to move it to it’s new home.

Basically I feel way over my head and am in desperate need of help. I think importing a blog from a different platform would be easier!

Please Help!