Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
You will have to go blind - there are no service manuals issued for Fuji cameras, apparently, or very few available, and I could find any YouTube videos or other instructions for the AX model series, even.
Remove *all* screws you can reach from the exterior. Then remove one parts of the 'shell' or outer casing. Find the connector that matches that of your replacement (a fairly good guide, if it definitely is for the Fuji AX655), disconnect that connector, remove anything fastening the LCD screen down, and make sure to note down any odd parts I haven't mentioned, as to how you removed them and what screws where etc.
For more apposite instructions, well... think about how possible it is that something else is wrong inside the camera, making the effort somewhat in vain if it's something else that can't be found or is expensive.
There really is no video instructing how to take apart an AX-series camera, even. But there seem to be two screws on either end, more or less, and removing those four then seeing if any case/shell part comes loose, then going on from there with my instructions (if you can photograph each stage and post me photos) we'll try to get the whole process right in detail.