There are two possible ways to become a Recognized Member in a collective. The collective's Admin(s) can invite you to become a Recognized Member, or in some cases, members of a collective may receive automatic invitations based on their recent activity.
The best way to qualify is to join a collective, and provide accurate and high-quality answers to questions within the collective. This will allow you to show up on the collective-specific leaderboard, which is one of the tools that will be used by collective Admins to recruit Recognized Members.
Recognized Members may have their role removed by the Admin(s) of the Collective, or via automated processes based on low activity.