So many ways to respond to this question...
My opinion is that parents create the environment and provide the opportunities and it is up to the child to develop a passion or not. Have music present and accessible from infancy onward. Have toys that allow for motor skill development and musical (subjective term at that age, of course) expression. Play your instrument(s) and foster an appreciation of music.
I am a believer in the Suzuki method, and like that it brings attention to having respect for the instrument as well as introducing instruction in music. Violin is a good starter instrument, specifically with Suzuki. When my son had the basics of reading sheet music and fundamentals, he transitioned to piano and began receiving instruction. It is important that the instructor knows how to relate to children. Make it fun and make it challenging. My two kids are 14 and 11, and the older continues to take piano instruction (8 years and running) and he chose to take up percussion in school band. The younger plays drums and just started back in with violin after a 4 year break with it, upon his own idea.
I took piano instruction at six years old and liked but didn't love it. It did teach me music fundamentals and a start on reading sheet, and after dabbling in trumpet I took up guitar at fifteen. The one thing I wish I had focused on, and have tried with no success to push my kids into, is voice training and singing. In hindsight, I would have put my kids into chorus early.
That's my experience. I'm interested in what others have to say.