Self Service Distribution Group Management

In order to add/remove owners/members of groups that you are an owner of, you need to do the following.

In New Outlook, click the settings gear in the top right and go to General > Distribution Groups
Click on the link to the portal
Users would sign in with their regular accounts and they can view the groups that they belong to and the ones that they own. Within this, they can add owners/members to the groups that they own and have permissions to edit.

If users are using Old Outlook, there is no clear and available means of doing the same thing anymore. The recommendation would be to go to Outlook on the web and follow the same instructions as above.