they are connected by a router, yes?
turn sshd on for both the remote computer.
rsync -rvP user@remoteComputerIP:/where/your/file/is /where/you/want/it/to/go/
This should do it.
Or you could try scp, but scp won't recover from errors like rsync will, so I suggest rsync.
Also, read the man pages on rsync to get more info on options.