How to get my website files onto HostPapa server?

Hi,

Apologies if I've misunderstood, but I can't see how to get my existing website files onto the HostPapa server with an FTP client while my domain name is still pointing to the people who used to host it.

The HostPapa FAQ says:

Once your web site files and emails are setup on our servers then your domain name needs to point to our servers in order for your hosting to be live at HostPapa. The process of pointing your domain to our servers is called, redirecting your Domain Name Server (DNS) settings.

I can't access the HostPapa server with my FTP client to upload the files, though, presumably because the server address (my existing domain, that I'm transferring across) is still looking at the old place. The instructions I've quoted above seemed to me to suggest that I should transfer the files before redirecting the domain name, but I seem to be caught in some sort of trap...

Can anyone please explain? Many thanks for any help.