[This is from HP.com]
This document explains the basics of installing or replacing the print cartridges. It is for a 5940 which is the same printer design, yours may look a bit different but I copied this from HP at the section for your printer so follow the instructions and you should be okay.
Insert the print cartridges
The printer shown below is the HP Deskjet 5940 series printer. Your printer might look slightly different.
Turn the printer on. The cartridge cradle will not move if the power is not on.
Open the printer cover.
Figure 1: Open the cover
Wait until the print cartridge cradle moves to the right side of the printer and is
idle and quiet.
you are replacing a print cartridge, press down on the print cartridge
to be replaced, and then slide it out of the print cartridge cradle. If
you are installing print cartridges for the first time, go to the next
Remove the new print cartridge from its packaging and carefully remove
the plastic tape. Hold the print cartridge so that the copper strips are on the
bottom and facing toward the printer.
Figure 2: Remove tape
1 - Protective tape
Do not touch the print cartridge ink nozzles or copper contacts.
Touching these parts will result in clogs, ink failure, and bad electrical
connections. Do not remove the copper strips. They are required electrical
Slide the print cartridge at a slight upward angle into the cradle until the cartridge
snaps into place.
Figure 3: Install the print cartridge
Repeat steps 3-4 for the remaining print cartridge.
Close the printer cover.
The printer automatically prints a calibration page.
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