Here's some info I found:
"First of all, gather together some supplies. You will need a screwdriver, thin wire cutters, a thin butter knife, a pair of scissors, and a replacement cable tie. A good tool is also a small flashlight. You will also need clear Scotch tape.
Firstly, you must take out at least one of the batteries out of your Furby. Next, flip the Furby upside down so you are looking under the tail or mane. You will see a large bump under the fabric. Take your scissors and cut the threads that hold the fabric together that covers it. Take your wire cutters and pull at the plastic cable tie. Cut the cable tie with your scissors and pull it out. Next, cut the threads that keep the ears on the plastic sticks. Then, peel up the fur as far as you can. You will notice that the plastic face plate that surrounds the eyes and mouth is connected to the fur. You must peel up the fur high enough so you can see the bottom of the face plate. It the face plate is screwed on, take your screwdriver and unscrew the screws holding the face plate on. If the face plate is glued, gently pull on the glue. Snap the face plate off. Afterwards, peel the fur straight over the Furby (there may be some glue holding the fur on at the back of the Furby, so work on getting that off).
After the fur is completely off, you will see a black case. This is the "skeleton" of the Furby. Look in each of the tiny holes in the black cast and unscrew the screws in them. Then, the black case will be able to separate into two parts; the right part, and the left part. Gently un-attach the microphone from the right side of the Furby.
In front of the Furby, right near its tickle sensor, there are two silver screws on either side of a plastic piece. Unscrew these screws and take off the speaker. Next, look through the clear plastic on the front of the microphone for a small piece of copper wire. Put the Furby's batteries back in and play with the wire until it seems as though the Furby is talking correctly. Then, tape the wire down in place. Then, screw the speaker on, replace the microphone, put on the skeleton, and snap on the face plate or screw it in, and GENTLY replace the fur, securing it at the bottom with a replacement cable tie. Sew back on the ears, and you're done!!! Make sure you replace the batteries!"
From
http://www.geocities.com/ali_furby/