Are you connecting via Wi-Fi, if so then use the password for your Wi-Fi network. Installing a printer is incredibly simple if you follow the directions. I'd first recommend stopping what you are doing and follow Apple's instructions in Printing Overview OS X Lion
Just got an HP 8600 printer. When I get to point of "password to allow HP installer to make changes" it won't accept any of my passwords, and there is nothing that says "check here to get password" Help????
It's looking for the password for an Admin user on the machine (probably you) use the one you log onto the computer with