1) Go here to start the process. Selection of distribution is the key here, you must select Ubuntu/10.04--HP's support for Mint lags quite a bit and they show Mint 8 (Helena) as the latest. Fill in the printer info and click download to redirect to mirror for download, then click Back to get HP's install directions page.
2) Open a terminal and change to directory you downloaded the file. You should see one file downloaded, in my case, named "hplip-3.10.5.run" Following HP's instructions (on web site) type "sh hplip-3.10.5.run" on command line. This should create a new directory to extract the file contents to, verify the file integrity, and extract the file.
3) Select installation mode "automatic" by typing "a" and Enter. You will be prompted to close any running package application (Synaptic).
4) The installation will correctly detect you are running "Linux Mint 9" and ask for confirmation. This is where you need to say No! Type "n" to get some menus where you need to select "Ubuntu" (should be option 7), and "10.04" (should be option 13). The installer should respond the "Distro set to: Ubuntu 10.04."
5) Type in your user password when prompted.
6) Read the Installation Notes, then press Enter to continue. As I have a network printer, I disregard the statement about having to quit the installer before the printer setup stage...direct connect printers will have to actually do that, but that comes later.
7) Get some coffee, tea, etc. while dependencies are being downloaded and installed. (Note this requires an active Internet connection.) This will take anywhere from 5-10 minutes (seems longer) depending upon what's missing. My missing dependencies (I installed Isadora 5 days ago, not many updates):
Wait some more for optional dependencies.INSTALL MISSING REQUIRED DEPENDENCIES
-------------------------------------
warning: There are 7 missing REQUIRED dependencies.
note: Installation of dependencies requires an active internet connection.
warning: Missing REQUIRED dependency: gcc (gcc - GNU Project C and C++ Compiler)
warning: Missing REQUIRED dependency: python-devel (Python devel - Python development files)
warning: Missing REQUIRED dependency: cups-devel (CUPS devel- Common Unix Printing System development files)
warning: Missing REQUIRED dependency: libusb (libusb - USB library)
warning: Missing REQUIRED dependency: libtool (libtool - Library building support services)
warning: Missing REQUIRED dependency: cups-image (CUPS image - CUPS image development files)
warning: Missing REQUIRED dependency: libjpeg (libjpeg - JPEG library)
At some point, the installs complete and you will see a warning that a previous HPLIP is installed or running and the installed will run an "apt-get remove" to get rid of the components, which may or may not work. Mine failed. The installer then states the new installation will overwrite the old components.
Keep enjoying the coffee, tea, etc. as now the build/make commences.
8 ) Just about there...build and post-build compete, you get a message prompt saying "RESTART OR RE-PLUG IS REQUIRED." This is where you have to decide what to do based on what printer you're attempting to connect. READ the ENTIRE message! If using USB-connected or parallel-connected (OMG!) you will have to quit the installer and reboot your computer. If network or wireless printer, you can type "i" to ignore and continue to the setup program.
9) If you typed "i" for ignore, you get a message telling you to ensure the printer is turned on. If you rebooted, return to a terminal and type "hp-setup" (already installed in /usr/bin). In either case you get a GUI set-up window to allow you to set up the printer you likely already have set up. In my case, I chose to manually install rather than risk any goofiness with a search as that requires only the IP address of the printer--easy to get from the Control Center -> Printing panel. The installer fills the printer name string, leaving you to fill in the description and location strings. You can print a test page at this time as well.
You're done! You will probably wish to have HPLIP start up automatically: Menu -> All -> Accessories, right-click on HP Device Manager and select "Launch when I log in."
[EDIT] Of course, now that I try to find it again, it's disappeared from the menu. I found that selecting "HP Device Manager" for auto-launching starts the full toolkit--when I wanted only the systray to start automatically. This is done by going to Menu -> Control Center -> Startup Applications -> Add, then adding command "hp-systray" with the desired name and comment strings. [/EDIT]
For me, the entire process took less than 30 minutes...much less time than writing this.