Go to Voicemail (using the usual shortcut icon)

Enter a phone # for setting greeting.

Click Record until satisfied (and be sure to Save).

Admin - 

Can access permissions settings for Voicemail under Admin>Phone Management>Edit Phone Numbers

Generally, anyone can listen or acknowledge voicemails for #'s they are assigned to.

We recommend setting a specific individual or group for those #'s where you wish someone to set a greeting.

Note: If no greeting is set, or if it is 'deleted', it will revert to the default.