While you can assign new supervisors while defining an assignment or a job slot, it's faster to have all of your supervisors pre-defined. By marking a supervisor as inactive, VSys will show that supervisor at the bottom of selection lists, making it easier to quickly choose the supervisor(s) you need.
From the Setup panel click on the Supervisors link.
Add new supervisors by clicking on the Add supervisor link and then locating the person to use.
Remove a supervisor by right-clicking on their name and selecting Remove as supervisor. Note this is only available for manually-defined supervisors, meaning those who are not attached as supervisors to any assignment or job slot.
Mark a supervisor as active or inactive by right-clicking on their name and selecting Make active or Make inactive. This is available for all supervisors.
Right-click on a supervisor to edit them, send letters, or any other actions normally associated with a person.
Click the Save button to commit your changes. Note changes you've made by editing the supervisors themselves were committed immediately.
VSys supports having supervisors being automatically added here based on their being on one or more lists. If you have complex criteria or just want a bunch of people to be considered supervisors without having to add them here, use that mechanism in system preferences ("Consider people on these lists to be supervisors").