Rodger,
If your desktop and notebook are networked, and the HP is hooked into the desktop, this is fairly easy. You need to make sure that "file and printer sharing" are enabled on both the desktop and notebook (found under the LAN Connection Properties). You also need to "share" the HP (right click on the HP's icon in Printer and Faxes). Finally, your notebook needs to "find" the printer. If the desktop is already "mapped" to the notebook, this should happen automatically (if it doesn't happen right away, and you don't feel like waiting, reboot the notebook). If the desktop isn't networked, that needs to be done first.
What you're asking about is exactly the configuration that I use. My desktop and wireless router are upstairs. My HP is connected to my desktop, and my desktop is connected to the router, and everything is networked together. Lastly, and this seems kind of obvious (but not to some people), the desktop has to be running in order to have access to the printer from the network.