Hooking the silent spinner to the cage bars isn't too hard, but this wheel is junky overall and definitely a bit frustrating!
So take the wheel, and you'll see a yellow cap in the center like below
Now unscrew this cap. Now you should see a screw, pull the wheel off of this screw
Then what you have left is just the attachment, hook this to the cage and put the wheel back on
Now simply screw the yellow cap back on and you should be good! The same concept works for bin cages. I used this same method to hook up this silent spinner to Duncan's bin a while back