All that is left to do is wire up everything, which is not as difficult as you might think.
Mount your shutter release button inside the costume where the shutter button will be. Cut a hole over the button so that when you press down on the costume's button, the shutter button is clicked. You'll have to use a lot of tape, and/or build a little shelf for it to sit on, to keep it from coming loose when it is pressed. Run the wire through the back of the bucket, to the inside of the camera.
Run your flash extension cord up through one of the hollow sides of the flash assembly. Mount your flash on the back, as far from the diffuser as possible for the best possible diffusion of light. Tape the cord along the way, so the tension of the cord doesn't move your camera off-center once it is mounted inside the bucket. You want some slack inside the bucket.
Run your USB through the back of the bucket, inside the costume, around to the back. This might best be done after the computer is installed on the inside, but you should wait until the very last step to install the computer body, because you don't want to risk the weight of it pulling too much on the monitor cable.
To install the laptop body:
Install the body of the laptop vertically on the inside of the costume, directly behind the LCD screen, but ensure that the screen cable will reach correctly. Plug the laptop screen back in, and tape the computer body up VERY HEAVILY.
There won't be much holding the computer in the compartment, other than the bottom edge of the costume, the tape, and your body pressed against it. You do not want the computer come loose, because if it comes loose, the monitor cable can break, and if it comes really loose, it can fall out completely. Be sure to cut holes around the fan units and leave them uncovered from tape. Also, make sure you leave clearance for your USB, and power cable.
Mount the camera:
I used a small tripod to mount my camera inside the bucket. This kept the camera lens near the middle of the costume lens, to prevent the edges of the bucket from showing in the photos, and also provided a solid base for the camera, so it wouldn't twist/ tilt after it was installed. I just glued and taped the legs of the tripod down to the inside of the bucket.
Be sure to mount it far inside the bucket that your camera lens doesn't touch the costume's plexiglass lens when it rotates during auto-focus. Be sure not to mount it too far in though, or you'll see the edges of your bucket in the photo.
For this step, you will need:
Lots of tape
hot-shoe extension cord
remote shutter release button