This really belongs in the networking forum, but:
Ordinarily, both laptops would have wireless - standard on the Mac, I have no idea about the VAIO. In that case, the Airport Express is connected to the cable modem, and you need to tell the Airport Express to talk to the cable modem and have that open up the internet connection. You do that via the Airport Express setup utility that comes with the AEx base station.
If the VAIO has no wireless card, then it needs to be connected via cable.
The AEx MUST be connected via Ethernet cable.
Now, you mention that the cable mdem has ethernet and usb. Is it possible to connect the VAIO via USB and have the AEx connected via ethernet at the same time?
If not, you'll neet a router to talk to the cable modem and split the connection among several computers. You can get a decent Netgear or Syslink router for around $40.