Gary DeMar wrote a three volume set called God and Government. I am reading through the first one now. In the second chapter, I found the most clearly articulated summary of what elders' duties are. This a paraphrase from p. 41.
Elders are to
1. Guide the church away from sinful behavior.
2. Guide the church to doctrinal purity.
3. Guide people to repentance.
4. Expel those unwilling to repent.
5. Restore those who are truly repentant.
6. Settle disputes among believers.
I would love to hear opinions on this list and whether you think that your elders, bishops, pastors, shepherds (or whatever you call them) spend most of their time doing these things.