The first step in helping a young child modify undesirable behavior is to set expectations with the child. Explain clearly and often your expectations or "rules" for classroom behavior. Instruct your child to answer questions only after raising his hand and being called on by his teacher. Repeat these expectations often, even after you see the behavior begin to change. Help your child understand that talking out of turn in school is not only disruptive, but it actually steals opportunities from other children who also want to learn and participate. Explain the problem of talking out of turn in terminology that your child can understand. Relate it to sharing toys, for example. Explain that "answer time" must be shared with other children too, giving everyone opportunities to participate.
Enforce your expectations with both positive and negative reinforcement. Tell your child at the outset what the consequences will be for talking out of turn as well as what the rewards will be for talking only after raising his hand and speaking when called upon. Identify what your child enjoys and reward him with those things as well as praise when he follows instructions. Use methods like time outs and removal of privileges when he speaks out of turn.
Practice the kind of behavior you want your child to display in school at home. Every night, maybe around the dinner table, or during breakfast in the morning, have family conversations where you ask questions and practice having your child raise his hand and answer after being called upon. It could be as simple as "What are we eating for dinner?" or "What's your favorite food?" or "What would you like for desert?" Engage your child in role playing often to help him learn the behavior you want him to display. Focus on modeling the type of behavior you want your child to display by avoiding interrupting others yourself.
Let your child's teacher know what you are doing to try to correct the problem. Ask the teacher to inform you about your child's progress weekly and to let you know when he has a particularly good or bad day. Consider working as an aid in your child's classroom or simply sitting in on class one day to discretely observe how your child behaves. Be consistent in the application of the training as well as consequences and rewards and in time, you will see an improvement in your child's behavior.