Don't kill a mob someone else is killing. If someone else is there first, they have 10 minutes to prepare to kill that mob. This "ten minute rule" begins at the time when the second person/group announces an intention to invoke the rule. Delay by the first person/group in acknowledging the secondary claim does not delay the onset of the 10 minutes.
In high-stakes situations or any other instance where a dispute seems likely, it's a good idea to ask for an immortal to come serve as a witness to the proceedings.
Note that each group, regardless of the number of players and pets within it, may only claim ONE specific mob, not a room of mobs. If it's a wandering mob, someone within the group with claim should use the 'follow' command to follow it, and remain awake and standing so that they will be in immediate pursuit of the mob at all times should it happen to move; if they do this, they guarantee their claim for the full 10 minutes, regardless of who else may follow the mob and/or be in a room the mob walks into. Note that this *only* applies to wandering mobs -- for all other mobs, you (or at least one player helping you) must remain in the same room as the mob at all times in order to retain claim! Pets *cannot* hold claim under any circumstances.
Claim stealing is a serious offense. For a first offense, the punishment is typically a fine of 3x the mob's gold plus having an official warning logged against you. Severity of punishment will increase with each offense, however, so if you make a habit of stealing other players' kills, be prepared to face more severe penalties. Stealing from mobs to which others have claim is considered stealing from players and will be punished accordingly.
You may NOT cast spells to aid a mob upon which others have claim, whether they are currently in combat with it or not. This is considered a form of harassment and/or PK, and will be dealt with accordingly.