A Fitting can vary from fitter to fitter. Most of the time you get what the above poster described. Some people fit statically, some fit dynamically.
Things to look for in a fitting-
Will you be hitting off of a lie board? This is the correct way to get your true lie angle.
How many combinations will the fitter use? The more the better. If they only have a few, then your really limited to what you even can be fit into. Some big companies have fitting carts with 50-200 options, while others like Henry Griffitts have up to 4000.
How long will it take? If they say it takes 15 Min's, I would find someone else.
Do they evaluate your swing, looking also at your current clubs? This is important to understand why you swing the way you do, if you need to correct anything before getting fit, and if you can adjust your old clubs...or get rid of them. A good fitter/teacher is ideal.
Will you be hitting indoor on a simulator or outdoor on a range, or both? If indoor on a simulator, you want to make sure its an accurate one. There are some out there that do not measure correctly, so it will give poor readings. You need to either have a very accurate Sim, or be on a range to test ball flight.Ideally both.
Will the clubs you will be hitting be the exact same specs as your receive? Check out the tolerances, they vary from each manufacturer.
Make sure you actually get to hit the clubs with all the combinations put together
Do they fit dynamically or statically? Should be the same price, but dynamic fitting is much more accurate.
Those are some key things to look for in a good fitting.
Good Luck!