So - you've got this blog/website thing going, and you set it up using Ghost! And now you need to find yourself a new provider – and you cannot stop thinking whether you could do it all by yourself!?
Export all your content
Make a tarball of all your images - from content/images - in my case the path was /var/www/blog/content/images
Now follow this recipe
Import your content
'cd' into the proper 'content' folder and
tar xf images.tar
That's how easy it is to move a Ghost based blog/website/thing