Honestly, the best person to ask this question of is your fitter.
There are different ways to approach bike fit, and the approach will largely depend on what you tell the fitter in terms of your goals for the bike and the fitting. Is speed/power/aerodynamics most important? Comfort? Do you have an injury or biomechanical issue that you need to deal with? How you answer those questions will dictate, at least in part, how the fitter will proceed.
Ideally, your fitter will start with a series of questions to determine how you ride, where you ride, how long, how fast, etc., etc. They'll also hopefully ask if you're experiencing any pain or discomfort on the bike in its current set up. They likely ask about your other physical activties, injuries, and the like.
From there, they'll likely take some measurements. My fitter started with my shoes and cleats (be sure to bring them, along with a pair of shorts and ideally a sleeveless or form fitting jersey as you want your fitter to see your body as you're on the bike) and went up from there in measuring my legs, calves, femurs, arms, shoulders, etc. They might also test for hamstring and low back flexibility, strength imbalances and the like.
Then the set up will begin. Your fitter will have your bike on a trainer and will liekly make some adjustments and then have you pedal for a bit. Then he'll make some other adjustments. If there are any parts that need to be swapped out, e.g., a new stem, he might make some suggestions.
What you can expect from the fitting depends on how honest, detailed and clear you can be from the start. A fitting will hopefully optimize your comfort, efficiency, and power (although you often have to compromise to some degree among those three things). A fitting will not make a bike that is fundamentally too big or two small for you suddenly fit, but it will hopefully iron out any kinks on a bike that is essentially the right one for you.
Be sure to ask what their policy is for follow-up visits. Some include it in the price of the original fitting so you can feel free to go back if something isn't working for you or if your body/style of riding changes.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher