When you see a griefer, they will purposely destroy things to make them look ugly. If you don't like that, here is a blog to help you!

PLAYERS:
When you see a grief of any kind, call a staff member over. If they are not there, just /mail them. If you do not have access to that command, just tell them next time they are on.
NEVER EVER EVER fix a grief unless a staff member tells you too. If they have rollback, you can be a suspect! If someone comes on saying that they are from Planet Minecraft, Bukkit or if they have reported a client fault, plugin problem or permissions error etc. tell an admin to mute them immediately.
Protect your house at all costs! Don't let griefers grief at all. If you find a deep mine with random caves that seem to go all over the place and no nearby (diamond) ores, tell an admin immediately as the mine has been x-rayed to find illegit diamonds!
Go to griefing sites like Nodus and look around. If you find the server listed, copy the link and show it to an admin immediately! Also recommend the plugin Core-Protect.

Staff:
Make sure you have the plugin Core-Protect on your server. If any player comes on claiming they are from PMC, Bukkit, a reviewing team (unless you applied for a review and they are trusted) or if they report bugs in permissions, craftbukkit, a plugin or the client, mute them on the spot and tell them that they are here to grief. Do not ban them just yet. Deop them just in case, whether they are op or not. Use Core-Protect to scan all griefs on the server and ban/warn all players that grief.
Be very careful who you give a staff position to, as they may just as well be a griefer! Here are a few tips to detect a griefer

1. They are impatient while waiting for their staff position
2. They try to get the highest rank possible!
3. They don't read the rules or staff requirements.
4. They sound VERY professional
5. They will be extremely nice to players

If these signs are shown in any player, google their username to see if they have ban appeals, griefing site accounts or any history on griefing. If they havent griefed for over 4 months, they should be all right. If you have MCBans, globally ban any heavy griefer and inspect these players for past global bans. A griefer may claim to be a friend in real life to a high staff position (An op/Co-Owner) and say that they want to help out. NEVER EVER EVER EVER EVER EVER op these people as they are massive scammers. They will grief you at all costs. If the server suddenly becomes laggy, '/killall' and inspect the mob spawning. If no success, tp to all players. If a player is over 1000 blocks away from the furthest warp (excluding outliers) they are running as fast as they can as far as they can to lag your server up. Please limit your map!

Thats it for now, any more tips will be added later!