|Because she already has a modem with a ethernet out cable, is there any hardware she needs other than a wireless router and wireless network cards for any PC intended to connect to the network?|
No, that will be all she will need.
And is it necessary that the router be a DSL router. Or will any wireless router do?
Any will do. There is no such thing as a "DSL Router" or a "Cable Router". The router itself doesn't know whether you're getting your internet from DSL, cable, wireless or a satellite. All you need to know is the connection from your modem goes into the WAN port on the router.
My thinking is that since she already has a modem, I can conect it to a router via the ethernet cable, and at that point it is functionally the same as a cable/broadband system, with which I am familiar.
Is that right?
Indeed it is. As I said above:
Internet >> modem (cable/DSL/wireless/satellite) >> router (WAN port) >> clients (either wired, or wireless)
I highly recommend when you get things setup that you enable WPA encryption on the wireless network. This will prevent outsiders from using your network.
Most, if not all SOHO routers are very easy to configure and setup and will come with a manual and setup guide. Read them through before you begin the setup so as to familiarize yourself with all the important aspects.