In theory the using Deskjet can be just as simple as connecting it via the USB cable and it works. However when I tried this, the printer was recognised but it refused to print at all. Apparently Tiger comes with the latest HP driver already installed and which is used by default (v 3.3). However I had to change the driver to Gimp-Print v5.0.0-beta2 (in the Mac Printer Setup dialogues), then all worked well.
Please note YMMV