They are not chosen, if someone wants to create a team, needs to have a minimum budget established, talk with FIA and Bernie Ecclestone, needs to have their own plant and for new regulations to build their own chassis and for the engine, they can choose from hire another team as their suppliers or build their own. It is a really though and complicated proccess in terms of money and regulations. If they succeed and are accepted, they will receive money each race from F1 organizers, not a considerable amount for the money they really need to be in constant development.
If your question was referred to the team drivers. They are chosen by team managers, and normally for drivers who have succeed in minor categories with excellent results or political issues as an example some Japanese drivers who are there because of Toyota or Honda.
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