How do you apply for a new Social Security Card?

Assuming you already have a social security # and need a replacement card you may goto your local Federal Building with the required IDs/proof of identity.

You can also mail such as well. Personally I've used a State College ID card that I mailed to the Social Security Administration, and they mailed my replacement card (and even my other ID back too).

If you're starting from scratch, visit your County Clerk's office and obtain a copy of your Birth Certificate. The Birth Certificate will be enough to satisfy the identity requirement to obtain a replacement social security card.