Like I said, all the info I found was from searching these forums.
www.joomlapolis.com/component/option,com_joomlaboard/Itemid,38/func,view/id,13872/catid,34/
This tells you pretty much what I mentioned, to copy your existing tables into the new databse tables via phpMyAdmin or something similar.
Try using google to search for database migration, and whatever you use with your database (phpMyAdmin, etc)..you might find explicit instructions there.
I myself have not tried it because I believe I am going to go through my webhost, I am fairly certain that they have a setup that does it automatically. However, if that fails, I'll definately be attempting to move the tables myself.
Hope this helps. And yes, I think your webhost DOES know what they're talking about.