Battery placement varies for the many different versions of the hp printers, as gleaned from the many posts here. For the hp Officejet Pro L7580, the battery is on the right side of the printer.
1) Remove the power and USB cable from the back.
2) Remove the two torx T-20 screws from the plastic panel that surrounds the power and USB jacks.
3) Open the printer top to the second level (below the glass) and remove the one torx screw.
4) Slide the right side panel off to expose the green circuit board.
5) The battery is on the medial (toward the middle) side of the circuit board, so the circuit board has to be removed from the frame. Remove the 6 torx screws.
6) Gently pry (you may need a small screwdriver for some edges) the circuit board out. Be careful not to overly stretch any of the electrical wiring when handling the circuit board.
7) Flip the circuit board over to expose the battery, in my case, a CR2032. Pry the battery out with your fingers.
8) Fashion an insulator to fit between the terminals. I cut a disk out of an old bicycle inner tube. A disk cut from an old plastic credit card should work; just don't include the magnetic stripe! Insert insulating disk.
9) Put everything back together and test.