vBulletin Manual - Adding or Editing a Moderator

To add a new moderator, go to Forums & Moderators > Forum Manager > Add Moderator in the Moderator column.

Forum – the forum that this user will moderate. He or she will also be able to moderate any child forums.
Moderator Username – the name of the user that will become the moderator.
Change Moderator’s Primary Usergroup to – if you wish to change the user’s usergroup when the become a moderator, you may do so here. The most common setup is to put all moderators into a Moderators usergroup that will then have access to a special forum.
Make Moderator a Member of – if you do not wish to move the moderator to a different usergroup but instead wish to add that user to one or more groups, making them a secondary user in those groups, you may do so here.

All other settings should be self explanatory. If you are unsure of an option, simply click the inline help icon for a further explanation.