Go to your Contacts app and select the person for whom you want to add a birthday. This is in landscape, by the way...
(1) On the right side, at the bottom left, select the Edit button.
(2) Then, scroll all the way down to just above the red Delete button and press the "add field" button. You will get a pop-up.
(3) Scroll all the way down on THAT one and, near the bottom will be the field "Birthday."
(4) Press it and you will be given the date input wheel to add the date.
(5) When you've finished adding the date, press the blue Done button at the top right and the popup will close.
And that's it, you've entered a birthday. Rinse and repeat for any other names and that should do it. Good luck and let us know how it works out for you.
Marilyn