It depends on the game size, game type and your personal preference. I have seen games that use automated scripts for almost everything and games that have huge staff with everything checked by humans. Some games might promote cheating (market feature, gift feature, etc) while others might maki it almost pointless (no way to send struff to others, no way of stealing things). The game size is important, if you have only a few hundred active players you can do almost everything yourself, when you have thousands it might not be possible anymore. But most of all it depends on your personality I think

Anyway, you probably need to cover these positions (you might be able to automate/outsource/ignore some of these):
- support (answering players questions)
- forum/shoutbox/chat/IRC moderation (delete posts/ban users from using it)
- tracking cheaters (scan for IP/transactions/etc)
- punishing players (jail/ban/remove goods/delete account)
- communication (post ingame announcements)
- payments (dealing with payments/donation issues)
- emergency (usually someone with full admin rights to do everything)
- staff management (add/remove helper/moderator/admin rights, staff forum management & other inner communication organisation, inner problems ressolving)
- misc (testers, promotion, artists, coders, hardware admins, etc)
Tools of the trade (in order of importance, IMHO of course :-D):
- staff structure (who is responsible for what, who is allowed to do what, chain of command, rules, code of conduct)
- your personal time investment (you will need huge amount of this)
- people (obvious

)
- staff forum (I have 2 active staff forums, one made by me, second made by helpers themselves, I think their forum sux but they seem to like it better

)
- moderator/admin panel (it is crucial that it has various levels so not only moderator/admin but various levels of these)
- your interpersonal/leadership skills