Two screws are hidden underneath two rubber feet highlighted in red.
Use the tip of a spudger to pry the rubber feet out of the lower case.
Depending on the age of your device, the rubber feet may crumble apart as you pry them out. If so, use a fine-tipped tool to scrape out any stuck pieces of rubber.
Carefully lift the lower casing from its bottom edge.
The lower case is still attached to the motherboard by the volume and SD board cable highlighted in red. Do not try to completely remove the lower case of the DSi yet.
Pry the volume and SD board cable up from its socket on the motherboard using a spudger.
Once the cable is completely removed, then you may take off the entire outer casing.
Use your fingernail or the edge of a plastic opening tool to flip up the retaining flap on the following three ZIF sockets:
Lower touchscreen cable
Lower LCD cable
Power board cable
Be sure you are prying up on the hinged retaining flaps, not the sockets themselves.
After flipping up the locking tabs on all three sockets, use your fingers or a pair of tweezers to gently pull the cables straight out of their sockets.