There really isn't a specific test they do. First, they eliminate everything else, such as Lupus, Gout (sp?), thyroid problems, and a bunch of other things.
For example, my doctor has run every test he can think of, and everything has come back normal. He has referred me to a rheumetologist, who I see next month, and the rheumy will either find something that my regular doctor didn't, or he will confirm Fibromyalgia. It's a long and frustrating road because you have to go through a bunch of other tests before some doctors will even begin to think of Fibro.