Instructions
Look on the game box and identify the publisher. You'll find the name on the bottom right corner of the front cover. You will need to know who published your game in order to seek a replacement.
Find proof of purchase for the faulty game. While Nintendo and most third-party publishers have some sort of disc replacement policy, you won't get far if you can't prove you purchased the game.
Contact the game publisher for a replacement (see "Resources"). While third-party publishers have their own terms for disc replacement, if the game was published by Nintendo and purchased within 90 days of the game's failure, Nintendo will replace the game free of charge---as long as you can provide the disk and proof of purchase.