In the "Instructions for Candidates Offered Admission" booklet they have (among others) the Birth Certificate Information card. They don't expect you to mail the Birth Certificate to them in that...do they?
As you can tell by now, there will be multiple items to send back to admissions. Include the card with the birth certificate in the same envelope with other items you're sending in.
I suggest you make multiple copies (where possible). Send the original to West Point. I made a folder (with accordian-type pockets) to send a copy of each form with my d for R-day. (In case WP didn't have it on file, she had one with her, and she'll be able to add any other important papers to it.) I also have a file of copies here at home - also just in case.
And I bet you thought the application process required a lot of documentation.