All City, State, and Regional Championship tournaments are open to the public. If you can get there, you can play. Local residency is not required.
National Championships are also open, with the additional rule that you must be a current resident (not necessarily a citizen) of that country. You may be required to show proof of residency before you can be registered.
The World Championship is by invitation only. You qualify either via a top Premier Rating in your age division for your zone (top 25 for North America), reaching a top position in a National Championship (top 8 for United States), or via the Last Chance Qualifier (top 4 are guaranteed invites). Also, the top 4 in each age division from the previous year's World Championship are invited back. Complete details can be found here.