Hit ESC anywhere in the game and click "Toggle player 2"
You might also want to customize controls after that. I think best way to play is if player 1 uses keyboard and mouse, and player 2 uses a controller. Or two controllers.
...Basically experiment and find what works best for you.
Viewing post in Light of the Locked World jam comments
Yes, it's possible for both players to play using one keyboard. To do that, you must select "Use keyboard" in player 1 and player 2 control option. Then remap keys so that player 1 would use WASD to move and player 2 would use arrow keys for example.
Be aware of button limit though - in some setups the keyboard only registers up to 4 button presses at a time.
If you have no controllers I recommend using Player 1 - Keyboard and Player 2 - Mouse.