After all of the lists have been received, a computer matches applicants and programs. At noon Eastern time, on a fateful day in March of each year, all applicants across the country receive an envelope telling them where they will spend the next several years. Controversy has surrounded the Match algorithm in recent years, due to a slight preference for residency programs in a very small percentage of cases. The algorithm has since been changed to favor applicants' preferences. There are several books about residency and the Match.
Several specialties have their own matching programs.
Consult the matching programs' web sites for schedules. A fellowship is a period of training that you undertake following completion of your residency, as a means to subspecialization. The list of possible subspecialties is almost endless. A fellow is considered somewhere in the hierarchy between residents and faculty. They are paid like advanced residents, but nothing close to what a private physician makes.