Hey Tamara,
If you are an administrator for your particular ArcGIS online organization you can add or delete members as well as change roles and other features. You first want to log in to ArcGIS online go to the "My Organization" tab. Here you will see a list of all the members of your organization. If you click the gear underneath the "Action" heading there is a drop down where you can delete members. It is important to note you may want to first disable the member in order to retain any of there content that is useful for your organization, once that is transferred over you can go ahead and delete them from your organization and that will open up a spot for your organization. To invite a new member go to the "Invite Members" tab and you can either invite a user with a ArcGIS online account or you can go ahead and create a new profile valid in your organization and simply give that individual the information.
Thanks,
Eric