JFrame or applet: do you want to write it for a browser, or a desktop application?
the rest: check what the game 'does' what rules it has. I assume you'll have a number of CARDS, so write a Card class, give it a type (spade, diamonds, ...) and a value (1 -> 10 || jack || queen || king )
then ... well, I have no idea what the game is supposed to do, so .. happy coding.
If you want this to be a learning exercise that builds long-term Java skills then starting with the details of parts of the GUI is leading you down a bad path. You'll end up with mess of spaghetti where the logic of the game is buried in multiple action listeners and nobody will understand it.
stultuske had good advice - start with his Card class, then build a Game class that contains the rules and has public methods for whatever decisions the game requires, and lets you query the results/current situation etc. Test and debug this by hard coding some plays and printing the results.
Then build a GUI that accesses an instance of Game and calls its methods to make moves, get the results etc.
For more detail on why this is a good approach, Google "Model, View, Controller" or MVC.