Great power, great responsibility and dA groups
Just to explain before you start reading, this is an editorial written by me so the suggestions detailed below are my suggestions. I am not the oracle and this isn't an official dA tutorial. You are welcome to agree or disagree with me as you please, and I hope some people out there find this useful.
Clarity of Information
Make your joining and submission process, and any limits to it, VERY clear. People who have been in your group since it launched will have a good understanding of what can be submitted where and how often, but new or prospective members need to be able to find all guidelines easily so they can adhere to them. The more information your members have easy access to, the less time you'll have to spend repeating rules to people who have made mistakes.
Knocking down language barriers
Do your best to explain everything as clearly as possible because not everyone on dA will speak the same language as you. This is especially important when rejecting submissions as it's very easy to seem rude or thoughtless when the real problem is a language barrier. If you aren't comfortable explaining things to people who you don't share a language with, check out #GlobalTutorials
to find bilingual deviants who may be able to help.
Honesty and skill levels
No group admins are out to intentionally embarrass or insult anyone (or at least they shouldn't be) and no artist seeks embarrassment or insults, so be honest about the level of art which will be accepted in your group. If your mission is to help lesser known artists get more exposure, say that. If your mission is to gather a gallery of professional level inspirational art, give prospective and new members that information before they join the group or submit their work. If you are going to decline submissions based on your personal taste, be honest about this.
You, as a source of information
Be available to answer questions or point people in the direction of useful information. You will receive notes and comments asking for clarification and while you may have explained this often, the person contacting you is only asking for help for the first time. You may receive notes to your personal dA profile too, which may not be ideal, but it gives you an opportunity to answer someone's questions and then let them know that they are welcome to send notes to the group rather than your own account.
You, as an inspiration
As the admin of a group, there are people who will look up to you. Remember that you are an administrator in a section of dA which attracts a lot of attention and to new, inexperienced or younger deviants you represent an admirable status. When people ask you for help, information or approval they aren't doing it to bug you. They're doing it because they think you're the best person to ask. Don't underestimate your influence or the effect that your words and actions can have on others.