Admin Responsibilities Summary - Guide

Most Concise Admin Guide: 

Have fun, do as much for the team/group as you can, don't be a jerk, and treat others as you would want to be treated

The guides below are published here as an open source community guidelinse and the admin team here is free to update this first post.

Feel free to copy, modify and post to your HQ group, but please include credit.

Version 11/3/2019 (Club Admins)

https://www.chess.com/clubs/forum/view/admin-responsibilities-summary-guide

Admin Responsibilities Summary - The short version

1. Set up a HQ for swift seamless communication. 

2. Decide who is doing what. Have a discussion with them and don’t just dictate.

3. Be prepared to have the occasional disagreement.  You are all human. 

4. If you have rules in place, ask the other(s) for feedback. Cooperation is a 2-way street.

5. Don't tell your admin(s) one thing and do something else. Mixed messages lead to confusion. 

6. Have fun. You are all volunteers at the end of the day. 

Admin Responsibilities Summary - The original and longer version

1. Keep members safe: monitor content

Monitor that posts on group notes, forums, news and team match pages does not violate the rules of your club. Either delete inappropriate posts or ask the user to do so. Either way, best to communicate to user in PM about why his/her posts violate chess.com community policies or the rules of your club.
https://www.chess.com/clubs/forum/view/chess-com-community-policies-5

You may wish to have admins from different time zones so you have some admin coverage through the day.

2. Recruitment of more members

Use invite feature to invite more members to group. Some groups may wish to attract high rated players, some active members (points measure posts and such). Another thing to look for would be a person who is not already member of too many groups. Finally, some groups have a rule that you need at least 30 day's history on chess.com before you can be invited or could join.

3. Organize Team Matches, Tournaments and Vote Chess

Some groups focus on discussions and may not have these. If you have team matches, fun to post group logo and battle cry to team match pages. Same for tournaments which also allow for custom trophies to fit your team's theme.

4. Keep group alive

Make regular posts to group notes and forums to keep group alive and encourage same for it's members. As discussed elsewhere, if you copy a forum from another group, ask for permission first and give credit.

5. Welcome new members

Not necessary, but nice that every time someone join an admin greet and welcome him/her on group note. Some groups use the "welcome to our group" fun trophy or post to the new member's personal notes.

6. Collaborate with other admins in HQ

Best practice is to have a separate admin Head Quarter (HQ) group where logistics, strategy and conflicts within the admin group can be addressed.

7. Recognize contributions by other admins and members

Consider things like congratulate the first member who wins a game in a team match. Further, a good idea is to give a fun (personal) trophy or post on someone’s personal notes if they create a new nice forum or make other contributions to the group.

8. Monthly newsletter

Very few groups have this, but if you do it will make your group stand out. Topics could include call for joining vote chess and matches, match statistics, reminding members of group philosophy, mini bios of members, jokes, etc.

9. Do not get burned out

If you have a day job, remember not to get overly involved and obsessive about all then group's details. It is supposed to be fun and it may be more so for everyone if you are relaxed and accepting.

10. Share responsibilities within the admin team

It may help to have different admins be responsible for different areas such as "Recruitment", "Team Matches", "Vote Chess", etc.

11. Cross Train

Be sure admins can cover for each other during sickness, vacation, etc.

Whatever you choose.
When there's a rule break - and if and when you and your admins want to do something about it
the idea of an HQ club is you don't have to re-post the offensive material again - in your main club.
That's what I meant by 'stuff'.  
Many clubs have an extra HQ club.  Many don't and prefer to get by with PM's (personal messages)
or to trust whatever admins/superadmins to handle things on the spot at the time.
Can work in a small club. 
Its my observation that the larger the club - the more an HQ club is needed.
But that's just what I've seen.  To each their own.