Here is the Social Security website and information about applying.
Social Security Number and Card
You can download the application and either turn it into a local office or mail it in.
It was really fast to get a duplicate card for FD. I don't know if it's your first one.
It's pretty easy to make an appointment. Here's the telephone number from the SS website:
By calling 1-800-772-1213, you can use our automated telephone services to get recorded information and conduct some business 24 hours a day.
If you cannot handle your business through our automated services, you can speak to a Social Security representative between 7 a.m. and 7 p.m. Monday through Friday.
Good luck!