If you can’t turn on or sign in to iMessage or FaceTime - Apple Support
iMessage uses the Internet, so the first thing to do is to check that your child's phone is connected to the Internet. You may need to select your home's WiFi network and enter your WiFi password, or turn on cellular data.
It also sounds like you need to have SMS messaging service through your cell phone carrier.
Once iMessage is turned on, the phones will need to be connected to the Internet for any messages to go through right away using the blue iMessage bubble. If either phone is offline, you may get a "Not delivered" message, and the option to either "Try again" or "Send as Text Message" (the SMS way associated with green bubbles).
What is the difference between iMessage and SMS/MMS? - Apple Support