A large number of questions that I get are about my opinions on when a child is deemed ready to begin lessons. While there are no hard and fast rules, there are some pointers and signs that you can use to determine when your child is ready to begin lessons.
One cannot magically deem a child to "be ready" for lessons at any given point. More important is the idea that the child needs to be tuned into music from early on - from the age of 5 is a good starting point. It doesn't matter if you want to start a musical genius or if you simply want your child to be delighted with the wonderful sounds of serious music. Perhaps the single easiest and best thing you can do to get your child ready to begin lessons is to expose yourself and your child to lots of classical, jazz, and other forms of musically sound and well performed music together. An appreciation of good music will help get and maintain your child's interest.
How wonderful for the child to be hearing the music of Bach's Violin Sonatas to Chopin's Etudes, Mozart's the Magic Flute, or Beethoven's Pastorale Symphony as well as the jazz/improvisational sounds of Art Tatum, Oscar Peterson, Chick Corea, George Shearing or Gary Burton!
One does not need to have to spend thousands of dollars investing in a huge CD collection. Having a radio station tuned in to the sounds of the great classical and jazz composers is an excellent way to develop knowledge and appreciation of good music with rhythmic patterns. The harmonics, and melodic ideas already well established in the child's musical ear will segue into lessons easier because the child can see a well-defined goal for the lessons.
There are varying opinions as to when a child should "officially" start lessons. Give a good deal of thoughtful consideration to the fact that, the younger the child is when beginning lessons, the more involved the parent will have to be with actively helping out with practice time, attending the lessons and being positively involved during the lessons. Generally, the child should be able to recognize numbers 1-5, and understand the correlation between the numbers on the page and the finger numbers. If the child knows the alphabet letters of a through G that is all that is required from a beginner. Most beginning books will spend a lot of time reinforcing these skills, so don't be too concerned if the knowledge is not always perfectly articulated.
There are of course exceptions to any and all claims of appropriate starting ages for children. For piano, I have had some excellent students start as early as 4 years old, and then others were not really ready until later - some not until adulthood!!! As far as violin students, I would suggest that the child needs to be at least between 10 and 12 and there needs to be a certain amount of maturity and responsibility to practicing. Wind and Brass instruments need to be children who are in grade 5 at school and up. Any younger and you risk damaging their developing lungs. Voice students - I ask that they can read very well - as they need to be able to read the words to the songs. Just about any age person can learn how to play a musical instrument, if they are very determined and the desire is great. Don't let your expectations and desires be the sole determinant of when the child begins lessons or how fast you feel they should progress. The most common frustration of the parents arises because they have forgotten that their child is taking the lessons and doing the practice. Remember that the child is a child, not a miniature adult. If the previous exposure to music has been going on for a long time, and if the parent(s) have reasonable expectations for their child taking lessons, it should be a positive and life long endeavor for all involved.