Growing up on Macintosh computers, I always feel a little crippled on my basic computer knowledge. I’m not good with DOS. I didn’t know, until recently, what an IRQ was. I had no idea how to make a bootable MS-DOS disk for ghosting. I didn’t know how to copy files between Linux systems, but I could writeup some IPchains no problem. Odd.

So anyway, here’s the command that you run on the server you’re copying FROM:
scp file_name user_name@ip_address:/directory_listing/
SCP: Secure copy
File_name: the name of the file you want to copy
User_name: name of the user with privs to the directory you’re copying to
Ip_address: IP of the server you’re copying to
Directory_listing: starts with / and doesn’t need a trailing /

In my case it’d be:
scp bigfile.iso ituser@10.1.2.2:/home/ituser

EDIT!!!!

There is also a program called WinSCP that allows you to move files back and forth with an FTP-style interface. I highly recommend it to those who use Windows.

EDIT 2 April 11, 2015
Obviously I should have included Rsync:
rsync -ru /src/dir/* root@remoteserver:/remote/dir/other/dir/