Well, once you pinpoint a potential mutation on a gene - that gives you a starting point into the pathway that could be possibly producing this particular disease. From there, it's sort of like clicking outwards from a wikipedia page, except instead of wiki pages, its related genes. Every one you go to, you read and find out what people know about it. You then start to form a picture in your head as to what the mechanisms of action are for this particular gene - what it does and how it is regulated.

From there, you build your model for how the gene works, and do some knock-outs / knock-ins, test it in various cell lines, verify the kinetics, try to find out the 3D structure. Really, anything you can do to get a handle on how this actually works in the system. It's quite normal for people to spend their entire PhD studying the mechanism of action for a single gene!