I did not know that you could check the queue of documents that are waiting to be printed on a network printer. This is assuming that the computer is using Windows 7 and the printer is on a Windows network.
From Start, open Devices and Printers and your network printer should be listed here. Right-click on it and choose See what's printing. The dialog that pops up shows the current document printing on this printer and also any other documents queued up to be printed on it.
Tried with: Windows 7 64-bit