You sign at the bottom of the return in Part II. The taxpayer, executor, donor, or an authorized representative must sign. If your last return was a joint return, your spouse must also sign (unless you have indicated by checking the box on line 1 that you are establishing a separate residence).
This form is not sent in as part of your Form 1040. It is mailed separately. You will need to print it, sign, and mail via first class mail.
For more information, including where to file, please see the instructions for Form 8822 at the following link: https://www.irs.gov/pub/irs-pdf/f8822.pdf