How do I open a Fuji F460 digital camera case?

The shutter button is not part of the rear case.
You haven't stated why you wish to open the camera?
There are 3 plastic clips along the top of the camera that you will need to release before the rear case will lift clear. The way to do it is to apply enough presure along the crome bezel on the top to release the clips.
They should be spaced apart evenly, 1 at each end of the camera and one in the middle. The hardest 1 to unclip will be the 1 by the shutter button. To release this 1, open the rubber cover for the usb port and you should see in the top right corner by the crome bezel a tiny gap where the plastics do not meet. With a pair of pointed tweezers ,or similar tool , insert into the gap and lift the rear case clear of the clip. NOTE, There are small components under there and the capacitor for the flash so be carefull! you could short this cap out and get a shock. There is insulation under there to prevent shock or short circuit and you have to watch what you do but it is the simplist way to unclip it. I have a photo guide for this model and it is freely available but I'm not supposed to add my email address.
daveward712 (at) aol.com

Dave - camera repairs
March 2010