Read-Only permissions

Click your calendar and then from the menu, select Share Calendar

An email will appear that allows you to send a sharing invitation and choose permission levels of access

Adding other permissions (Author, Editor, Custom)

Like any other Outlook folder, you can right click the calendar, select Properties and Permissions to have granular control over access levels.  Outlook 2013 also has a Calendar Permissions button on the menu, when in the calendar view.

This will allow you to add/remove users and control the permissions more specifically.  It includes inbuilt roles, such as Editor and Author.

Choosing a permission level will alter the different check boxes to explain what it does.