To add someone as your delegate, click "File" tab, on the left the "Info" category should be selected by default (if not, click it), on the right, click "Account Settings" button.
Select "Delegates Access" from the drop down list.
The "Options" window pops up, click "Delegates" tab (last one), then click "Add..." button.
The "Add Users" dialog box pops up, search for the person whom you want to be your delegate, click to highlight the person's name, then click the "Add->" button in the lower left corner, and then click "OK".
The "Delegate Permissions" dialog box pops up, in which you can set up permissions for the delegate that you selected. By default "Editor" is selected for Calendar, who has full read, write and modify permissions for your account. You can also set the permission as "Reviewer" (who has read only access) or "Author" (who has read and write access) depending on what you need the person to do.
By default, the option "Delegate receives copies of meeting-related messages sent to me" is selected, click to uncheck it if you don't want the person to receive meeting request for you. Set up permissions for other folders (Inbox, Contacts, etc.) as you desire, then click "OK".
You'll be back to the "Options" window, select how you want the meeting requests/responses to be received:
You can add more than one person as your delegates. When you're done with adding people and setting permissions, click "Apply" button then "OK".