To manage a calendar other than your own, the calendar owner must share the calendar to you with permissions to Make Changes to Events or Make Change AND Manage Sharing.
The calendar must be shared to you with permission to Make Changes to Events or Make Change AND Manage Sharing.
When creating an event, use the Calendar drop-down and select the name of the calendar that you want to schedule from (see image below).
If you are scheduling on behalf of a person: Be aware that when the event is scheduled, the calendar owner will also receive an invitation so that they are aware that the event was created. However, that invitation does not require any action on the part of the calendar owner because the TOP "Yes" will already be selected.
Invitations received on behalf of someone else can be accepted/declined by clicking on the more details link in the invitation.