Moving Word Press blog files to another host provider…

Greetings All!

I’m a little tech unfriendly and need some help. I’m moving from one host service, Blogomania to another host service, Media Temple. Problem is – moving my files over (I’m learning) is not as easy as simply ftp’ing them. How can I move my blog entries over to the new host provider? Any help is so wonderfully appreciated.
Cheers, Felicia