From the tender age itself, you should let them know the advantage of financial planning and saving for the future as then they would carry the skill set pertaining to money management life-long.
And a good way, to start with it is by gifting a piggy-bank to your kid. Let them learn how little savings on a regular basis add up in a period of time. And accumulated sum would enable them to buy something of their need or want. Initially to inculcate the habit you can give a certain sum on a monthly basis and later ask them to save from their pocket money.
You can also instill the habit by creating a sample savings account of your child with yourself. You can ask the child that he/she can either have the allowance of Rs.100 now or Rs.150 a month later if they keep the money with you. The extra amount would lure the child to leave money with you and hence save.
Later, in their teens, you can open a saving account in the bank for your child and ask the kid to deposit the amount on his own to better acquaint him how the entire system works. Your financial behavior and actions will influence your child's action to a great extent, so in order to instill in them the habit of saving you should yourself set an example by saving.
Once you have succeeded in nurturing the habit of saving in your child, you can promote it further by rewarding him for his effort in the direction. As in the long run, it is not the amount saved in the initial years but the habit of saving that will ensure healthy future financial life for your child.