If you click the "Find" tab at the top-left of the page and enter "motion sicknes" you will find many threads with good information on the subject.
For someone prone to motion sickness I would suggest two things: get a perscription from a doctor for a patch that can be worn around-the-clock; there are many good over-the-counter remedies, but for a severe case I would consult a doctor. Next, book a cabin on a low deck and near the middle of the ship. The motion of the ship will be less noticeable there than anyplace else.
But assure your friend that the very large and modern ships today, with their stabilizers and gyroscopes, have very little motion. Most of the time you are not even aware you are on a ship. And in the rare case when you encounter severe weather or high seas, the patch should keep you very comfortable.