^^Well sort of correct. Switches are not dumb, hubs are dumb. Switches switch packets intelligently via destination address.
Now as to the OP's questions:
The way this works is modem-->router-->switch--->end nodes (clients). Things get blurred because the modem can contain a modem, router, wireless ap, and switch all in one box. What most home users have come to know as a router is really a router, wireless ap, and switch all in one box. The apple airport extreme is a router, wireless ap, and switch.
Assuming your cable or DSL modem is just a modem and not a router and switch your setup will be as follows:
modem-->airport extreme-->switch-->end devices