That is correct. I tend to like to leave the main desktop near the network equipment (DSL modem/WiFi Router) hard wired simply for speed reasons. I say leave it wired when wireless is not required that and its easier to troubleshoot when things go wrong.
A wireless router out of the box is pretty much plug n play. I would however setup security which would require to have at least one wired connection temporarily. These are the steps I would take.
1) Plug CAT5 cable from modem to the WAN port on your WiFi Router.
2) Plug a CAT5 cable from the router to your desktop.
3) Access the routers configuration page via a IE window. All routers are different so the IP addy may be differnt usually it will be 192.168.0.1 or 192.168.1.1.
4) Go to the WiFi setup portion and enable security. I recently used WPA-PSK with a key and it worked out fine. I chose not to go with WEP since so many people are cracking those networks.
5) Select a custom SSID, channel and operating mode.
6) Enter the security info on both laptops and they should connect with no problems.