When you sign up for an Overflow account, you start off being the sole member of your organization. You can go to the Dashboard (People tab) and add more people. Only Admins and Owners can invite and manage people. Contributors can only see the list.
To invite more people to your organization, click on the "Invite People" button. Enter the email addresses of the people you wish to invite. They will be receiving an invitation email asking them to join the particular organization. They are initially given the role of Contributor. You can change this from the person's settings.
In the People tab of the Dashboard, you can manage the organization's members. You can see all or filter by role, see which invitations are pending, resend the automated invitation email if the person hasn't responded or copy the invitation link for including in a custom email.
Finally, you can remove organization members. If their invitation was pending, then it is revoked. If the member was active, then you'll need to note that by removing them you will be revoking their access to the Overflow for this organization. Any data they had under this organization has to be transferred to someone else, or else will be deleted upon removal.
Note: Team members can be invited to join an organization at no cost during the free 14-day trial. After that, a seat has to be purchased for each member.