This information can be found in detail in the ASA Code in Article 516 Section G:
http://downloads.asasoftball.com/about/pdf/asa_code.pdf.
To simplify as best as I can, there are several different ways to qualify for the USA/ASA National Championship Finals in ASA. Generally, in Indiana, you are playing for a Local Association berth (registration berth), a Regional Qualifier berth, or a National Qualifier berth.
The Local Association berths are based on the total number of youth teams registered the previous year. Typically in Indiana we have between 2-4 of these available each summer for each classification, depending on how many registrations we received the previous year. Teams must be registered with Indiana ASA to be eligible for these berths.
There are 2 Regional Qualifier berths available to our region each summer per classification. These are on a rotation from year to year among the associations in the region (Illinois, Chicago, Indiana, and Kentucky ASA). In 2010, Indiana is able to award one of the 10A, 12A, and 18A Regional berths. Teams must be registered with one of the associations in our region to be eligible for one of these berths.
There is 1 National Qualifier berth available to our region each summer per classification. Like the Regional berths, these are rotated throughout the region associations on a year-to-year basis. For 2010, Indiana has the 16A National berth. Teams may be registered with any ASA association throughout the country to be eligible for these berths.
So, when a tournament is listed with a Regional or National qualifier designation on our tournament list, there are 2 berths available to be awarded in that particular classification in that tournament. These are awarded with the National or Regional berth going to the tournament winner and the Local Association berth going to the next highest finishing Indiana team.