connecting a single printer to TWO computers

I have a new HP computer with XOP prof. and an old SONY with XP home. I have one printer HP 950C and asingle monitor. I can switch between the two computers. My printer is plugged into the Sony USB. When I try to print when I am on the HP computer, nothing happens. The person fro Verizon FIOS told me this morning I must TWO wireless LAN adapters, one for each of the two computer. My question is this: I do have on hanf a new USB easy tranfer cable ; can I plug each end into the USB in each computer. will this work as aconnected network ? The Verizon person said that they do NOT get involved with mt setup. I have a wireless router, the two computers are coonected to the router by ether net cables. What is the solution?