Need to connect HP 3600n Printer to Two Computers...?

I am probably over thinking this and its easier than it looks...I have a desktop that my HP 3600n printer is connected directly too, I have another desktop in another office connected to the Internet and a wireless router so I have internet access on the other desktop also. My question is can I somehow network the printer that is connected to my desktop so that the other desktop can print to it also but without any cables running all over the place...in essence, I guess I'm wanting to print to the HP from the desktop that it is NOT wired too. I hope I haven't made this too confusing...thanks for any help...

Bjorn2009-09-29T12:26:37Z

So long as both of the computers are on the same network, connecting to the same router for internet, then you can use file and print sharing through Windows to print to one printer from both computers.

Here is a link to Microsoft's explanation on how to do it:

http://www.microsoft.com/windowsxp/using/networking/expert/honeycutt_july2.mspx

It works similar on Vista.