Wireless Confusion

Well, I'd like to build a wireless network system for my wife's birthday so she can remotely use her laptop. I don't want to go the ad-hoc method as our desk top pc would have to be powered up and I understand the internet access speed would be cut in half, so I think a wireless router is in order. My confusion lies in what is needed to build this system. I see that some wireless routers have several lan ports. Does this mean I can run my dsl to the router, then hard wire the router to our desktop and install a wireless card in her laptop or do I need a wireless adapter for BOTH computers. I've looked at several diagrams but none have this specific arrangement. Another bit of confusion is I noticed that back of my dsl modem has several lan ports. Can I pick off another port for the wireless router? All I want to do is share internet connections without leaving the desktop pc powered on. I downloaded the manual for a router I'm interested in but again, it wasn't clear to me how to do this (no diagrams). Thanks a bunch.
Crazylegs

 

Could be that your DSL Modem is a Modem/Router Combo.

However No what ever thr modem is, you do need a Wireless Router.

Computer that connect with wire do not need Wireless Card,

If the Modem is a Router the new Wireless Router should connect as an Access Point.

Wireless Router as an AP - http://www.ezlan.net/router_AP.html

A Wired/Wireless network look like this, http://www.ezlan.net/network/router.jpg

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That's great, Cat5E!. That's just what I needed to know. Thanks a bunch.
Crazylegs