You could also use CD-RWs and erase re-use the same disc over and over.
If you want to cable directly from your network card to her's, you'll need a crossover cable... It has a few wires switched around so you can direct connect two computers. Otherwise, you'll need a hub/switch betwixt the two computers, then you only need two regular network cables.
Easiest thing would be to share a folder on her computer, then install samba-client on your computer. You will be able to mount her shared drive onto your system, then transfer files back and forth. You can use the command-line, or get something like LinNeighborhood << www.bnro.de/~schmidjo/
>>, or use LISA in KDE, to be able to browse to her computer.
If you want to put the shared folder on your computer, and browse to it through Network Neighborhood on her's, you'll need to install the full Samba and configure it. Not too hard, really. Search the forum or Google for more info.