By default, administrators can do anything with mailinglists: send emails, add recipients, create new lists, etcetera. Normal users are only allowed to send emails. At the mailing list level you can refine this:
Both Users and Owners are set on the Lists tab of the Mailing List Assistant main form
If in the mailing list record the Users field is empty, all users can use this list. This is the initial situation.
You can limit which users have access to the list by entering their (login-) Names in the Users field, seperated by ';' for example: John;Pete;Kim
In the example only John, Pete and Kim will see the mailing lists.
If in the mailing list record the Owners field is empty, only administrators can edit this list. This is the initial situation.
You can specify additional normal users to have write access to the list by entering their (login-) Names in the Owners field, seperated by ';' for example: Mary;Andy;Kim
In the example Mary, Andy and Kim will be allowed to the mailing list's recipients in addition to the administrators.