In addition to the built-in IOS parental controls, you can fine tune iPad and iPhone safety by choosing the right browser. But in order for these kid-friendly browsers to be effective, you MUST disable the native iOS browser Safari and disable the installation of new apps. To modify these two settings, go to Settings > General > Restrictions.
Here are a selection of kid-safe iOS browsers.
Net Nanny Three pre-defined safety settings to get you started quickly, from the grandfather of Internet filtering software for families. $4.99
Mobicip Offers a Safari-like experience. Upgrade to a Premium subscription in order to build a customized filter. FREE or upgrade for $9.99 per year per device.
RangerThe filtering system uses a combination of blacklists, combined with customizable whitelists to create a filtering system that is updated hourly. Also allows you to determine hours when the browser can be used. FREE
MetaCert Browser Create custom selective filters to show only websites that you think appropriate. One time $0.99 purchase, no annual fee.