Membership in The Apache Software Foundation is a privilege and is by invitation only. Candidates for membership are proposed by existing members, and voted upon by the existing membership. Since the Foundation is a meritocracy, meaning that contributions and skills are the factors used to judge worthiness, candidates are expected to have proven themselves by contributing to one or more of the Foundation's projects.
The details of the process by which someone may become a member of The Apache Software Foundation are described in section 4.1 of the Foundation's bylaws.
If you would like to see what individual members are working on which projects, we have created a page where the ASF members can list what projects they are working on.