How do I add birthdays to my calendar so they repeat year to year?

Include birthday in your contacts using the Contacts app. Then in Calendar go to the list of calendars (touch the red Calendars at the mid bottom of the screen), scroll down until you find the Birthday calendar, and touch it so that it has a tick mark beside it. Not only will the birthday show up every year, it will even tell you how old they are!

Add the persons birthday to their information in Contacts. If you add the year of birth the calendar birthday will even tell you their age.