I've done it a lot as my D4160 has problems with older versions of hplip. But the instructions are long and complicated as they involve first what is not in their website instructions, that is completely purging everything hp from your system first.
I don't know which distro you use but in Debian I aptitude search hp and then aptitude purge and give it the list of hp stuff. Let it go ahead and remove whatever it needs to. In OpenSUSE, well just wait a few days and install OpenSUSE 10.3 and you won't need to bother uninstalling hplip or using installer script as it comes with the latest.
It is kind of impossible to get the new hplip installed over the ones installed by the distro's without purging the older stuff first.
Then you need to print out the installation instructions on the hplip website.
Follow the instructions for the automatic installer (that .run file you have) only if it supports your distro, otherwise download the tar manual install file.
Whichever, you'll need to follow the directions and get everything they say to install as dependency's, all those dev files, etc, installed even though they may have slightly different names on your distro.
You likely have some of it left over and installed already which is fine. That line they give to install it really doesn't work as they are named differently on different distro's. On Debian just do aptitude search for the stuff and then aptitude show for the different things to see what they are and see if they install some of the other stuff as dependencies or recommends, which aptitude includes by default.
Once you have that stuff in there you can go ahead and run the file. You right click it and in the Properties Permissions tab it should be read/write, read, read and make executable.
Then you do whatever it says to type into the terminal to get it to run, including any --switches the directions say to use.
It was a bit easier on OpenSUSE when I needed to do it there, as the installer is capable of downloading and using YaST to install what it needs on its own.
Do not run the installer as root! It'll mess things up! It will ask you for your root password when it needs it.
It really does a nice job of setting it all up. It runs hp-setup to install the printer when it's done. Make sure to follow all the instructions regarding what to do for its closing scripts when the install and setup is completed. It sets the right permissions, links and stuff.
Then, to further configure things hp-toolbox is terrific, with lots of tools for configuration, level indicators, print settings, etc.
For future upgrades you can use the installer (keep all the folders it makes where they are) to uninstall things but really, once you've used their installer the new versions can upgrade over what it finds. It'll remove some of it and just overwrite the rest with newer file versions.
I forget exactly the command to start it. But the instructions tell you. Stick the .run file in your home folder, open a terminal there and type in what they tell you. But purge the older stuff and install the dependencies first.