Interns, leaders, staffers, and admins can all be added in a signup record. Go to a signup record and click the "edit" tab. At the top of the right hand column in the "edit" tab is a drop down menu where you can change the signup's permision level.

Updated (09/30/2013): You now have complete control over which features are available to your team members with NationBuilder's permission sets. Learn more about how to create custom permission sets for your nation.