From the Prime Gaming site, you can browse through available games and in-game content. If you see an offer you're interested in, simply click the associated Claim button to begin the process (sometimes customers will claim a code to redeem content via a storefront).
Prime Gaming is one of the many benefits of an Amazon Prime Membership. As Amazon explains, With Prime Gaming, unlock instant access to tons of exclusive content for your favorite games, and a collection of PC games for free & each and every month.