Sunny is correct... here is a bit more detail:
The physician will first take a very careful history, including any past and present complaints that you have, any pertinent family history of disease, the places you have lived and visited, substance use (like tobacco, alcohol, drugs (legal and...uh...not legal...), herbal supplements you might take, vitamins..anything that is "non-food"), why you are seeing him (what are your major issues that brought you to the neuro).
Then he'll do an exam. Unlike other kinds of doctors, you'll probably not have to take off your clothes. He may examine your eyes to see if there is any damage of your optic nerve. He'll test for visual acuity, look for evidence of double vision, note if there is any incoordination of eye movements.
He'll test for evidence of weakness by asking you to resist efforts to pull or push your arms and legs. He may also have you squeeze his hand with each of your hands. He'll test coordination including a finger-to-nose test, in which you are asked to bring the tip of your finger to your nose rapidly, with your eyes opened, and then closed. Then a heel-knee-shin test, in which you are asked to move one heel up and down the shin of the other leg. He'll check your balance in a variety of ways, including asking you to place the heel of one foot directly against the toes of the other foot and move forward, step by step (the "drunk test"). He'll check for sensory disturbances by asking if you can feel a vibrating tuning fork he'll place on various parts of your body. He may pinprick you in areas to see if you can feel it, or if the sense is different from one limb to another. He'll test your reflexes, and see if they differ on one side of your body.
After all that, he may then schedule an MRI -- magnetic resonance imaging -- of your brain. As Sunny said, this is non-invasive. You'll go to a clinic (or perhaps a hospital) where there is an MRI machine. You'll be asked to lie down and then be inserted into the machine -- like a tube -- and images will be taken inside your brain. This doesn't hurt, but it is noise and confining. Some folks with claustrophobia find it uncomfortable, but it otherwise is not usually a problem.
You may also be scheduled for evoked potential tests -- tests that look at the spped and efficiency of the nerve impulses and signals in your brain. These are also non-invasive.
Finally he may ask you to undergo a spinal tap, or lumbar puncture (same test, different names). This is invasive, and uncomfortable, but if all those other tests prove inconclusive, this might be the one that narrows the focus for the doctor to try to figure out what is going on with you.
So before you go, you might want to gather up as much of your prior medical history that you can, and talk with any relatives about their medical history, so that you can tell the doctor as much as you can about past problems you may have had, or that might "run" in your family. You might want to gather up any meds and supplements you take, and make a list of them, the doses, when you take them. And then be prepared to have any of these other tests done (at a different time than this first appointment) as he and you figure out what is going on with you.
Good luck, and let us know how your visit went!
...I am not a doctor, nor health professional, and don't pretend to be one, here.....