This article explains how to set up an iPhone or iPod Touch so that your children can use it safely.
The iPhone and iPod touch require an Apple ID to set up and allow downloads from the iTunes Store and App Store. An Apple ID is also used for features such as iMessage, FaceTime, and Find My iPhone.
Your child can use your Apple ID, but in the long run it makes more sense to create a separate Apple ID for him or her (especially if you use Family Sharing).
Once you set up an Apple ID for your child, you can use that account when setting up your child's iPhone or iPod Touch.