How can I connect my dreamhost server to another remote server to download from the non-Dreamhost server?
It mostly depends upon what resources are available on the other server, as DH has a full compliment of standard *nix tools for such purposes .
From the Dreamhost shell you can use rsync and wget for example. Just make sure your user is “shell enabled”, log in, and go for it!
You need SSH, and after figuring that out if you haven’t already, do this if you are just trying to download a handful of files:
file.zip will be downloaded into the directory on the server you are currently in.