This document explains how to respond to invitations using Apple iCal (Mac OS 10.5-7) or Calendar (Mac OS 10.8-9).
When iCal/Calendar receives an invitation for you, which iCal/Calendar calls a Notification, a new icon will display at the top-left of the main iCal/Calendar window. It looks like an In-Tray with a downward pointing arrow. The number of invitations will also be displayed to the right of this icon. Also, on the View menu, the Show Notifications item will become available for selection. In addition, the event to which you have been invited will appear in the event window with a gray color surrounded by a white dotted-line. iCal/Calendar provides three response options: Maybe, Decline, Accept.
With your mouse click on the Notifications icon at the top-left of the main iCal/Calendar window. A menu will drop down on which is listed all the event invitations to which you have not responded. Click on the button indicating your desired response to each invitation.
This same menu can be triggered by selecting on the menubar View -> Show Notifications.
Double-click the event on the main iCal/Calendar display and the Info window will open. The invitation responses are at the bottom of the window.
You can also select the event to which you have been invited and from the menubar select Edit -> Get Info to also show the Info window.
If the Inspector window is open, click on the event to which you have been invited and when the Inspector window contents change, the invitation responses are at the bottom.
Note that if you select Maybe as your response, the event will remain in the calendar yet with a gray color which shows that it was neither declined nor accepted by you. In OS 10.9, these events will take the color of the main calendar with a gray dotted line around it.
If you select Decline as your response and you have Show Declined Events enabled (see the View menu) iCal/Calendar will continue to display the event.