Clipping is really easy. If your cards image has all the cards in a horizontal row, to draw card i
g.setClip(x, y, cardWidth, cardHeight);
g.drawImage(cardsImage, x - i * cardWidth, y, Graphics.TOP | Graphics.LEFT);
What you're doing is saying: set the clipping so that whatever graphics drawing methods I use, only the stuff inside this 'clip rectangle' actually gets drawn. Then you draw the cards image offset left so that the card you want overlaps the clipping rectangle, and only it gets drawn.
If you want to unset the clipping afterwards, use e.g.:
g.setClip(0, 0, getWidth(), getHeight());
If you forget to do this and try to draw other stuff afterwards, it won't actually get drawn. You will
make this mistake, but if you're prepared you'll spot it and fix it quickly