Printer on Vista

I am new on the Vista OS and have the following problem:
Problems with Printers in Vista. I have an HP printer connected to a Desktop running XP SP. My laptop’s OS is Vista Home Edition Premium I’ve added the HP printer to the Vista based laptop. The problem is whenever I want to print from the Vista Laptop to that printer, The document flashes momentarily on the HP printer window, then disappears and nothing is printed. I have no problem with printing to a printer directly set on the network. What could be the problem? Thanks for any help anyone could provide me with.