Apple doesn't charge you for Push, but it is not simple and not cheap to make and maintain your own push server, which you will need, if you want to send push messages.
Try PushWizard.com, a free and unlimited push service.
It can send 250 million push messages / hour.
PushWizard is free for unlimited devices, while other services can be very expensive if you have more, than 1 million users to reach at least ONCE per month.