By petitioning the court for a conservatorship of an incompetent person and asking that you become that person's conservator and providing reasons why you would be an appropriate conservator, such as the person's child, and demonstrating that you are a person of intelligence and integrity.
If you mean how does one get on a judge's panel of persons a court may appoint when there is no one else available to serve, I do not know. I'd ask the court clerk.