On first glance, it looks tricky but it really isn't!  Once you've done it the first time, you'll see how easy it is and a little practice makes you a pro.

1) Turn the stamp upside down and press in the two red buttons on the side of the stamp component.  While holding the buttons, push the bottom grey part of the mechanism into the stamp body until it locks into place (about 1 cm). You can then push on the ink cartridge to pop it out of the stamp component.

2) Insert the new ink cartridge into the slot until it clicks into place.

3) IMPORTANT: You need to clean the polymer disc before unlocking the body and before you use it again. Press in the red buttons again and push the component all the way in so that it locks again. Take a wet paper towel, wet wipe or damp cloth and thoroughly wipe off all the ink on the disc.  Make sure you use only water (no alcohol or other thinner as it will affect the ink) and then pat dry with a paper towel or dry cloth. 

4) You can now release the stamp by gently pushing the mechanism into the stamp body (don't hold the red buttons) and it will pop back into place.

5) Remember to replace the ink cap on the remaining cartridge so it can used again.