Google "Game State Management Java" or something along the lines of being similar. Game State Management is an abstract idea that you should get into the habit of grasping earlier on. This idea will apply to how to get your game objects(such as your jigsaw pieces) to move on a 2D graphics context or canvas.
Understanding the behavior of the coordinates of the graphics canvas you are working with. This concept will guide you in getting your jigsaw pieces to move correctly.
Google "Game logic Java" and "Game loop Java". Without this knowledge, you won't have a game.
Google "Loading and drawing images java". Without this, the player has no frame of object reference of what is going on in your game.
What kind of Jigsaw puzzle are you talking about? Do these pieces have weird sizes that needs to somehow click correctly with the other pieces with weird size? If so, this just another layer of complexity that you need to plan out before you code the actual game. Or are these pieces all squares?
Rather than code your jigsaw puzzle piece, I recommend Pong. It is far more realistic of a project to complete than the jigsaw puzzle given your level with 2D graphics that you stated.
I don't like to list tutorials because:
1) It does not facilitate thinking. It gives all the answers away which will hurt you big time in learning.
2) You won't lecture yourself or question what you are doing when you are programming a simple game.
3) You will not write your own code.
4) You will lose sight of the big picture.
But I did list keywords that comes up commonly in game development that applies to simple and complex games. So these ides will guide you in making Pong. You will need to struggle with it. i certainly did but I got better every day.
While game play is important, the flow of getting the game menu to transition to game play and vice-versa is just as important because it will make you appreciate the game as a whole package.