Does this Southwest Airlines gift card have fees or an expiration date?

It has no fees and no expiration date.

How can I apply this Southwest Airlines gift card toward a flight booked on southwest.com?

After selecting flights and entering passenger information, choose “Apply Travel Funds” in the payment section, then enter the gift card number and PIN and click “Apply Funds.” If the card does not cover the full total, pay the remaining balance with another form of payment.