My husband switched jobs in the middle of the year and overpaid FICA. How do we apply for a refund?

You show the excess payment as a credit for taxes already paid, on line 67 of form 1040. If you file form 1040A, include the excess on line 42 and write "SST" and the amount of the credit to the left of the line. See details on page 46 of Pub 505:

http://www.irs.gov/pub/irs-pdf/p505.pdf