Start/Control Panel/Hardware & Sound - there you'll find one entry for
Printer and another for Scanners & Cameras.
If you go to the actual item you can right-click and create a shortcut.

Isn't there a button on the scanner to do that?  If the software is
installed properly isn't there a menu item under HP for HP Director?  How
about opening something like a photo editing application and choosing to
scan that way?

I presume you mean in VISTA not in the XP you refer to for comparison?

What version of VISTA? The home versions do not have Fax & Scan so you
have to do it from the applications installed for the scanner, or other
applications that pick up a Scan or Capture entry in their menus.

I have an HP all in one, and also teach people how to use their
computer. I have found the controls for HP totally different using Vista
than they were on XP.
For the best way to use your HP to scan now, go to your start button,
and on the  menu you'll find, Windows Photo Gallery. Open this. Then go
to the top bar where it says File. You'll need to go down this list to
where it says import from camera or scanner. You will then be able to
scan, and edit all types of features.