Are you asking how people get invited, or how you specifically can get invited?
If the former, it's simple. A member just needs to call the Club and make reservations under a person's name. That will allow that person to attend a meal at the Club. The member does not have to be present at the reservation, but the guests' actions reflect upon the member so they typically choose carefully.
If you're asking how YOU can get invited specifically, start networking. Many large corporations have memberships. Do you know anyone that works for an organization that has a membership? You have an acquaintance that is going. What was their connection? You could ask them for advice. Make it known to all your friends and family that you'd love to eat there. Maybe someone knows somebody with a membership or a connection to a member.