You can do this with the scp command, which uses the ssh protocol to copy files across machines. It extends the syntax of cp to allow references to other systems:
scp username1@hostname1:/path/to/file username2@hostname2:/path/to/other/file
Copy something from this machine to some other machine:
scp /path/to/local/file username@hostname:/path/to/remote/file
Copy something from another machine to this machine:
scp username@hostname:/path/to/remote/file /path/to/local/file
Copy with a port number specified:
scp -P 1234 username@hostname:/path/to/remote/file /path/to/local/file