To add Pokemon to your card, type in their names in each of the text boxes below. Once you've typed in a Pokemon's name, its sprite will appear. You then need to drag it so that it's inside the black rectangle. The part of the sprite that's inside the white area of the black rectangle will appear on the trainer card.
Below, there are three buttons that when clicked on will show you the trainer sprites for that category. Click on the trainer sprite that you want and it will be added to the card below. Just like with adding Pokemon, drag the trainer sprite onto the card where you want it to appear.