You should create a GameServer class and a GameClient class. Game logic goes in GameServer and rendering goes in GameClient. If your game logic is mixed with your rendering code, take a look at some model view controller explanations (here's a decent article: http://www.badlogicgames.com/wordpress/?p=2668).
Let me tell you that usually the server and client are completely different applications and sometimes it isn't feasable to let the users host the server because it might involve configuring firewalls and whatnot.
So GameServer should extend Listener, create an instance of kryonet's Server, and add itself as a listener to the server. GameClient should similarly extend Client, create an instance of kryonet's Client, and add itself as a listener to the client.
If you pass a reference of the current game state class to the GameClient, the GameClient can communicate to it and tell it what to render and then the game state can tell the client what to send as input. Similarly, if you pass a reference of the current game state class to the GameServer, the server can provide input to the game logic and then the game logic can tell the server what to send to the clients.
I would recommend creating a simple message passing program on IP loopback to get familiar with kryonet.