You can also start out with Internet Connection Sharing ("ICS"):
http://windows.microsoft.com/en-US/windows-vista/Using-ICS-Internet-Connection-Sharing
But, the computer that is connected directly to the cable modem
needs to remain ON, in order for the second computer to access
the Internet via the first computer's ICS feature.
ICS will eliminate the need for a router, because the
ICS host will do the "routing".
Note that you'll still need a hub or switch (see diagram at link above);
and the host computer needs 2 LAN ports:
one to connect to the cable modem,
and the other to connect to the switch or hub.
If you have only 2 computers, I believe you can
eliminate the hub / switch, and wire the second computer
into the second LAN port on the host computer.
But, it's been a long time since I used ICS, so
please confirm this latter point yourself.
I do recall needing to revert to fixed IPs on
both computers, in order to stabilize ICS.
MRFS