The layup is the easiest shot and the first shot you should learn. It's not as easy as it looks at first, as a lot of kids have difficulty getting the correct footwork, and shooting off the correct foot. Then you must also learn to use either hand, and eventually do the reverse lay-up.
Footwork
When dribbling toward the basket, move slightly to one side of the hoop to create the proper angle. If you're on the right side, dribble right-handed, and plant your left (inside) foot and jump off that foot, and finally shoot with your right hand. As you raise your right hand, your right knee should also elevate. Pretend there is a string attached to your right hand and your right knee. Reverse this form if shooting from the left side.
As you approach the hoop, take a half step with your outside foot, then take a full stride with your inside foot pushing off the court. When jumping your outside knee should be bent. Go directly toward the basket, with your head up and eyes focused on the backboard. Go up strong and straight to the hoop. Don't shy away if there is a defender, just go strong to the hoop. You may get fouled and get a three point chance.
Aim
Always use the backboard ("use the glass") when shooting lay-ups from either side. Aim for the top corner of the box on the backboard. Focus in on this area; don't watch the ball. Keep your head up.
The Push Release
Younger players who are not yet strong enough for the underhand release should use the push release. Release the ball with the back of your hands facing you. Extend your shooting arm, as you push the ball to the hoop off your fingertips. You should go up with two hands, then release the ball with your outside hand. A very young player may need to shoot the ball with two hands.