Marian, there are a lot of ways to fix squeeks. The squeeks usually are from wood moving on a nail or a nail moving in a wood beam or joist. How you fix these depends on what access you have and it generally is easier and "prettier" to make the fix from under the floor. You can stop the squeeks from above, and these are usually in the "almost as good" category, but there are a lot of variations.
A good floor refinisher should fix the squeeks. For one thing, any open and loose nails can tear up his equipment and make the job tougher and more expensive for him. If he is the right guy for the job, you and he should be able to discuss this and he should guide you as to what he will do and what you should do for a better job. If you can't talk to each other, find another refinisher, but do accept that time is money for him.
One thing that you might want to check is an article about a year ago in The Family Handyman magazine on this subject. You might check your library for back issues. The drawings showed enough themselves to give you a great amount of information to make the right fix.