Gwent is an upcoming card-game based on The Witcher universe, and will be released for PS4, Xbox One and PC. The beta has already started for PC and Xbox One, but in order to participate you need a beta key. If you are luccky and got one, head to GoG and redeem the code.
In order to get a Gwent key you should firstly sign up at the Gwent website. This will add your e-mail to their database, and you might get lucky the new time they send out new keys.
If you cannot wait that long, there are other means to get your hands on a Gwent closed beta key. You can purchase a code from someone else who was picked from the random invites they have already sent out. Lots of MMO marketplaces sells these, as well as a lot of eBay members, so just search for a seller to purchase one. The price seems to be around $10 USD for one key.
You can also try your luck in the official Reddit Gwent giveaway thread. Lots of people post spare beta keys in there, so make sure to check it often and look for people you might want to give you a key.