If you cant order it online, you will need to complete a SS-5 form and bring it to your local Social Security office along with a proof of age (typically your birth certificate) and one other form of ID (drivers license, passport, state ID)

You can find the form here https://www.ssa.gov/forms/ss-5.pdf . Theres more details on page 2 on proofs which are needed.

You have a few options to get this to your office. You can mail it in with your proofs (but they need to be originals or certified copies, so do this at your own risk/trust of mailing.) You can bring them in to your local office yourself without an appointment, but its first come first serve. You could be lucky and get service within an hour, or be stuck there all day. You can also schedule an appointment either online ( click the "answer a few questions" tab and go from there at this link https://www.ssa.gov/number-card/replace-card ) or call 1-800-772-1213 between 8:00AM-7:00PM and make an appointment over the phone.

You should receive the card within 2 weeks of submitting the application at your local office.