Depending on the age of your child, you know that if you make them a big part of something interesting they are going to love it, take pride in it and learn more. Start by explaining to your child the importance of knowing what to do in an emergency and all about the 911 thing if you have not already. Set aside a day where you and your child will put together a first aid kit.
It should include band aids, gauze, adhesive, ice packs, peroxide, and alcohol, syrup of ipecac, scissors, soap, tweezers, cotton, calamine lotion, disposable gloves, paper cups, and matches. As you get these items together, explain what each one could be used for and have your child give you an example. There are first aid training classes for children of just about any age. They are not very lengthy classes and if there is a charge it is usually nominal.
Make a list of emergency phone numbers in case of an emergency and post them somewhere where your child knows where they are and let him know that these are available to him if he needs them but that he can not abuse this privilege. Quiz your child on how he would handle various situations involving medical emergencies. Have your child help you make a first aid chart and go through it together.
You may have to start off with basic first aid training but there is no reason that your child can not know what to do if someone is choking, how to give CPR, how to stop bleeding by applying pressure, and various other things by grade school or in some cases even sooner.
Of course warn your child that this does not give him a license to be a doctor, not just yet anyways, and these procedures are only to be utilized in real life emergencies. For example, tell him that he may not call 911 because his sibling scraped her knee. Explain that if he makes calls to 911 when there is not a true emergency then he might tie up the lines for someone else who does have a real emergency.
Children are amazing in what they can learn and maintain in those little heads of theirs and when their instincts kick in also what they are able to do can be astonishing. As they grow, they will learn more about how to handle medical emergencies. First aid training for kids is a gift that you can give them that they will carry with them forever and who knows, maybe one day they will save your life.