Andrew Davis has written an article at the Gospel Coalition on how to run an elders meeting.
By the astounding grace of the Lord Jesus Christ, the elders have been entrusted with the awesome role of “undershepherds” of his flock. This ministry is done collectively; therefore, the elders must meet together regularly to carry it out. The elders must consecrate themselves to the glory of God and the good of his people, and carry out the shepherding, prayer, discernment, and management tasks entrusted to them. As they do so, they should conduct themselves as Spirit-filled men who seek unity and true understanding of each other’s minds.