How can I use a gift card on App Store?

If it's an iTunes gift card, as opposed to an Apple Store gift card (which can only be used in Apple stores and the Apple online store), then you can redeem it onto your account : http://support.apple.com/kb/HT1574

And as long as you are buying content for yourself (you can't use an account's balance for gifting content) then your balance should be automatically used for your purchases : http://support.apple.com/kb/HT5582

When making purchases, content credits are used first, followed by Gift Certificate, iTunes Card, or Allowance Account credits; your credit card or PayPal account is then charged for any remaining balance.

If it's an Apple Store gift card then it can only be used in Apple's bricks-and-mortar stores or their online store, it can't be redeemed onto your iTunes account. You might be able to use it to buy iTunes gfit cards - are you near to an Apple store ?