For beginners, the most important teaching of use of the weak hand will be for teaching dribbling. Teaching how to shoot with the other hand, especially shooting the lay-up or other finishing shots at the basket, will follow with age and experience.

In teaching dribbling, the primary concern of the coach will be to make sure that whenever a player is dribbling, anywhere on the floor, that the dribbler has his/her body between the ball and the defender. This will require dribbling with the left hand when moving to the dribbler’s left and dribbling with the right hand when moving to the dribbler’s right.

After we’ve spent the time needed to be sure every kid can dribble with either hand, hopefully without looking directly at the ball, then we begin to have them move around the floor with the ball, switching hands. To begin learning the concept of dribbling with the hand away from a defender, walk the kids through chairs or cones, having them dribble with the hand away from the chair or cone. (See http://www.top-basketball-coaching.com/January_2007.html )
(See http://www.top-basketball-coaching.com/teachingbasketballdribbling.html)

When it comes time to begin teaching shooting, I think most coaches will agree that we start shooting by teaching the lay-up/lay-in. The lay-up is the most basic shot in basketball. For the non-dunking individual, it’s the highest percentage shot we can get. (See http://www.top-basketball-coaching.com/teachingshooting.html )

For the beginner, even this seemingly simple shot can initially be daunting. This may be the first time a youngster has had to think about coordinating a hand with the opposite foot. It’s not unlike a child throwing a ball with the same foot forward as the hand they throw with. Not effective. Same thing with the lay-in—opposite hand, opposite foot or the shot process will be clumsy. So, I have a simple technique to get kids started thinking about this hand/foot relationship without having to dribble.

First, have the players stand and go through the motion of shooting without the ball using the dominant hand while standing on the opposite foot and raising the shooting side foot off the floor. Do this several times. Now have them start on the shooting side foot, step onto the opposite foot and lift into the air while going through with the shooting motion. Again, do this several times.

I now stand in front of the basket holding the ball out so the shooter can take it from my hand in order to shoot with the dominant hand. If it is the right hand, the shooter must take the ball out of my hand and go off their left foot, then shoot it off the backboard, hopefully into the basket. At first, I have them start on the right foot, step left and take the ball as they leave the floor. The left side will go off the right foot and use the same procedure. After they have some success with this, then I allow several steps and still have them take it from my hand. When I feel they have made the connection well enough between the hand and foot, I let them dribble in and shoot. The next stage will be to allow them to dribble to each basket in the gym and shoot the lay-up.

As players progress in their skills they will need to be taught to understand that they should be able to shoot lay-ups effectively with both the right and left hand. If driving to the basket on the left side of the floor, shooting a lay-up using the right hand is likely to get the shot blocked.

In an actual game, rarely will a player have the opportunity to lazily run to the basket and shoot an uncontested lay-up. Most lay-ups are shot while fast breaking with a defender on the dribbler’s hip harassing the dribble all the way to the basket. If lay-ups are practiced nonchalantly then in a game type situation players are more likely to miss the lay-up because they might jump off the wrong foot, or shoot the lay-up too hard because their timing is off. It's not logical at all for a player to make even the simplest of shots in a game if they are not practicing the shots the same way they would shoot them in a game. Make sure your players are using correct technique and that they are moving at game speed when shooting lay-ups in practice and during pre-game warm-ups.

Later, players will find that if they try to shoot the same type of lay-up in every situation they will lack the advantage. It's important to be able to shoot different types of lay-ups and finishing moves at the basket, with either hand, so that they will be harder to defend in certain situations. These will come with playing experience and a coach’s ability to teach as the players move up in age-groups.
(See http://www.top-basketball-coaching.com/November2_2006.html )