How should I store game data in a game server?

The server has to have a copy of the game state.

If you can reasonably expect that the game server will be up and running during a particular game, and that all interaction between players in that game will always occur with that particular game server instance, you can simply hold the state in memory.

If, on the other hand, you expect a server to only be alive during a distinct request from the player, or for requests from a player to be distributed across potentially-many game server instances, you'll need to store the state elsewhere. A database is a possibility, as is another singular server, or a simple file on a disk accessible by all server instances, et cetera. It depends on your specific requirements.

As you claim to be new to this, I would strongly suggest you pursue a model where there's one server per game and it's up for the duration of a game. It's a simpler model to start with.

Most turn based multiplayer games do still keep all game state in memory and have the server living and listening to the players; if you won't be constantly listening to the players and are going to set it up with requests i.e.: host your game server and send RPC/REST requests via HTTP(S) for the player moves, then a KV store like Redis or MongoDB would be a good way to hold the data in-between requests, preferable to an RDBMS because game state will be linear and your player moves and current state can be stored as Hashes (in Redis) and your moves list can be stored as a List (in Redis) so there's no need to use something like MySQL for its more powerful query system. Running a game server for simple card games over HTTP requests and storing state via a Key Value store would make it pretty easy to scale and support many games on one server and build a universal API for Windows, Mac, Linux, Web, iOS, etc versions of the game.