text: For the most part you are representing a country so you have to be a citizen of that country.  From what I know to make an Olympic team as a participant on a team sport, like basketball or hockey, you are invited to tryouts and the coaches choose from that group, who go to the Olympics.  For individual sports such as track and field, skiing, figure skating, and others there are Olympic trials where the top two or three finishers in each event make the team.