Exposure is very important. If you have friends whose children play, ask if you can their child would be willing to play for your child. (Many a child has taken up an instrument because an older friend or relative plays it.)
Your local symphony orchestra may have a "Petting Zoo" with instruments that children can try before a children's concert. If a child has never heard a clarinet, how would they know that they might fall in love with it.
If you do not have a piano, you might consider putting an electronic keyboard in the child's room. Those with musical samples where the keys go down as the music plays are particularly appealing to children, and you will often see them trying to pick out the tunes themselves or with the sample.
Consider leaving a trumpet mouthpiece around for your child to try to make a sound on. Some can do it easily; for others, it may take longer, but it may give them a sense of accomplishment.
Join a Kindermusik or parent-child music class where your child may have the opportunity to play mallet instruments and drums.
Remember: finding the right teacher is not always easy. For some lucky parents, they know a warm, friendly teacher who loves children and wants to share their own love of music. For others, it may take some searching.
How do you know it is the right teacher? It reminds me of my dog guru who, when we were ready to get a puppy, said, "Go visit the breeders. If you don't like them, you won't like their dogs." If you visit the teacher and don't like him/her, your child probably will not either.
Rule #1: Ask if you can come and meet the teacher to determine whether your child will be a good fit for the teacher.
Rule #2: Request a trial lesson. If your child comes home unhappy, things will probably not get better over time. (If they will not agree to this, I probably is not the right teacher.)
Rule #3: Remember that the first teacher does not have to be a world-class virtuoso; they have to love children.
Rule #4: The teacher must have a sense of humor.
Rule #5: The teacher must love children.
Rule #6: The teacher must love children.
Rule #7: The teacher must love children.
You want your child to love music. Perhaps they will be part of the audience when they grow up or perhaps they will play string quartets with fellow scientists on Thursday nights. Perhaps they will play in the college orchestra. Perhaps they will play in the town band when they are teenagers. Perhaps they will play simple carols for family Christmas parties when they are 9. And for a very, very few, perhaps they will discover that music is a passion and want to make it their vocation. But that is the rare exception. Most will simply have discovered world of sound that is filled with beauty and will reconnect with it throughout the rest of their lives.
There will be times when your children do not feel like practicing. Many years ago, the great violinist Izhak Perlman, was asked by a radio interviewer whether his children all played instruments. When he said yes, she blithely quipped, "Well, they must like to practice." To which Perlman said with a twinkle, "No one likes to practice!" Every day of practice is like working on a long-term project: little by little great progress is made. It is never smooth sledding the whole way. So,
Rule #8-100: You are there to be the cheerleader, the appreciative audience, the warm pillow when a performance goes poorly, the one who says, "You are doing a great job. Stick with it."
No adult ever regrets having stuck with an instrument, but countless parents over the years have said to me, "I wish my parents had not let me quit."