The below little VBS script is an example of how to pull back a list of network printers a users is connected to.
This script is only pulling back the server and share names but you could retrieve other properties in the same way
Set colPrinters = objWMIService.ExecQuery ("Select * From Win32_Printer Where Local = False")
If colPrinters.Count <> 0 Then 'If there are some network printers
For Each objPrinterInstalled In colPrinters ' For each network printer
msgbox objPrinterInstalled.ServerName & "\" & objPrinterInstalled.ShareName ' Show the server\shar name