That google suggestion yields this informative article. I feel reasonably confident I can figure this out. That tutorial seems pretty clear and I've already purchased a nearly identical Linksys router.
It sounds to me now like that article laserlight linked is really all about turning off all the features on your wireless broadband router so that it acts like a much simpler device, namely a wireless access point. I am now wondering if I might have just purchased a Linksys WAP54G. The price is the same as the router I linked before - which is puzzling because it sounds like a simpler device.
I also have this paranoid fear that the new router (configured as an access point) will be unable to communicate with any wireless devices that connect to it because its own DHCP has been turned off. I'm hoping (and the tutorial seems to suggest this) that the wireless part of the communication handled by the new router/AP is a separate thing from the delegation of IP addresses.
Oh well. I bought the stuff. I'll let everyone know how it turns out. THANKS for the help!