First, you need a mouse to hack. Not just any mouse will work, it has to be the kind that use mechanical rotary sensors. The only kind I know of is micro$oft model #31660, (the kind I used) but If you look inside a mouse, and it has shiny metal shafts, it shold work fine. I guess you could use a standard optical mouse, but it would be a lot more work.
Next, you need a piece of pipe with the same inside diameter as the youstick shaft. This will be used to couple the joystick to the rotary sensor. After cutting it to length, cut a notch almost all the way through, leaving just enough to keep it from falling apart. More on this later.
Don't for get to file all the rough edges off. You don't want to cut your fingers. They're needed to play Galaga.
If all goes well, the coupler should now look better than this. (I was lazy with the file.)
Take the rotary sensor, clamp it in the vice, and cut it's shaft down. Leave 5 to 10mm, or the width of the grommet. By now you should have the following.
Slide the grommet over the shaft. If its fairly tight, it wont need glue. If its too loose, add a drop of cyanoacrylate (super glue for you unscientific people). Put some glue on the outer edge of the grommet, and slide it into the coupler. Set the assembly aside to dry.
Clip off the end of the nail, put it in the electrical connector, and crimp it. If you used a crappy old connector that you found bottom of a drawer like I did, you should probably solder it as well. This will be our actuator.
Now, carefully bend the connector to a 90° angle, making sure it will still fit on a screw.
Next, screw the actuator onto the body of the joystick. You may have to remove a microswitch to do this. Oh, and be sure to leave to lowest notch of the joystick free.
If you didn't glue the rotary sensor to the coupler, remove it now, leaving the grommet glued. Slide the coupler over the joystick shaft and use a clip to secure it to the lowest notch on the shaft.
Replace the rotary sensor and carefully glue half a paper clip to the bottom, putting the end over the actuator. Make sure the paper clip sticks out far enough for the joystick to move in the opposite direction. It should now look something like this.
Thats it. You're done. Here's another pic.