My understanding is that she wants to get the printer to push out a page (while not actually printing anything) whenever a button connected to the Arduino is pushed. This would involve the Arduino pushing some sort of message back up the virtual serial port created when the USB cable was plugged in, and then having some sort of script, or whatever, on the other end listening out for that message that should then make the printer go. The script could be in Processing, or could be a simple script such as the IRC controlled LED example Fergal demonstrated in our Arduino classes last year.
(Direct drive of most modern printers (particularly most cheap modern printers) is virtually impossible with something as low-powered as an Arduino as most of the "brains" behind rendering pages have been farmed out to the host computer rather than having onboard support for PCL, Postscript or any of the other printer command languages as that adds cost)
If you were to go this way about it, you could get the listening script to print a blank page. Alternatively, if you don't value the printer, most have a form feed button (labelled in all sorts of different ways depending on the printer involved) that pushes through a blank page, which could be directly hijacked and routed to a switch, perhaps?