ok as for router, it is not necesary, jst a network cable would do (a crosover one, not a straight one) and just run knoppix on both computers. on one you start sshd and log in from the other.
if you already have a hub, switch... and a working network, no problem there then.
sshd alows the programs sftp and scp to log on to the computer running it and transfer files to/from it (it also alows ssh for remote administration).

to get sshd going you can run my scripts., one on each computer (sudo scriptname):
run first this on one.
Code:
ssh-keygen -t rsa -f /etc/ssh/ssh_host_key; ssh-keygen -t rsa -f /etc/ssh/ssh_host_rsa_key; ssh-keygen -t rsa -f /etc/ssh/ssh_host_dsa_key; ifconfig eth0 192.168.0.102 sshd; passwd knoppix
now the scipt below on the other.
Code:
ifconfig eth0 192.168.0.103; sftp [email protected]
to get them to run copy them to two text files and make them executable, that is chmod +x /search/path/filename (i have them both on a floppy).

just give the password and you can do cd (to change directory), put to put a file from your computer on to the other), get, eeeh well this s not that hard i guess...
cd /serch/path/to/file/
and then
get ./file
the first script helps generating the crypto keys, configure your networkcard, starts sshd and asks for a new password for the user knoppix.
the second script configures your networkcard, logs in to the first computer and you will be asked a few easy questions (in the style: do you realy want to conect to this computer?).

hope this helps. if you want more info just ask.