See -> Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support
You cannot disable WiFi or cellular data connections to the internet overall, but you can restrict access to only allowed web sites you enter, or disable web browsers.
Also Wifi and internet access is required for free iMessages between Apple users, and is useful for Find My and location tracking or sharing. A cellular data connection is necessary for MMS messaging, which means the device can also access the internet via cellular data but you can disable app’s access to cellular data and lock it so the user cannot change cellular data settings.