I tried that but I will run it again to make sure I did everything right.
The printer icon on the desktop now has a outstretched hand which I am assuming means that this printer is shared.
That is correct. The desktop now allows sharing of its printer.
Now, if you have not already done so, yo need to log on to the laptop while the desktop is running, and bring up the laptop's "new printer" wizard (or whatever Vista uses as an equivalent). Tell it to create a network printer; it will ask for a path to that printer, or it may be able to find the path itself. It will also ask you to give the printer a name. Once it knows where the printer is, it will create a network printer, to which you can then print.
At least, that's the way it works in WinXP, Win2K and Win98SE, none of which require any special driver software when setting up network printers; the drivers are only required for printers local to the machine on which they are being configured.