In order to set permissions when sharing your calendar, go to Calendar > Folder > Calendar Properties.
Figure 1: Calendar Properties Window
The Calendar Properties will appear, select the Permissions tab.
Figure 2: Calendar Properties and Permissions
In the Calendar Properties window, you are able to grant users various permissions that would enable them to modify or view your calendar when shared. You are also able to Add/Remove users from viewing your calendar as well.
If you would like to share your calendar with other users who are not listed already, click the Add button.
Figure 3 shows a list of users based on your address book after selecting the Add button. Select the appropriate address book and find the user you wish to add and click Add.
Figure 3: Add users to to Calendar permissions
After adding a user and applying permissions, share the calendar.
If the permission you have set did not happen immediately after sharing the calendar, check the permissions of the user and change them to fit your needs then click Apply then click Ok and permissions will be set.
In this example I will now assign Prospector Pete to have Publishing Editor permissions over my Calendar.
Figure 4: Assign permissions
By highlighting Prospector Pete's name and navigating to the drop-down menu below, I am able to give Prospector Pete various permissions. By choosing the Publishing Editor option from the drop down menu you will see some items are automatically selected granting and restricting access.
Figure 5: Assign permissions
Please note: You do not have to use one of the per-assigned permission levels; you may assign your own custom level of permissions using the check boxes provided.