Start out on kid-specific sites. The kids' section, which follows, lists a couple of them. Or use a children's Internet book. Most are written with that in mind. My first book was focused on keeping kids occupied and categorizing kid-related sites so they don't need to use the general search engines as much.
Nothing can replace the monitoring of online sessions by parents.
But software can help you keep track of how your children are spending their online time. Some local providers offer 'family accounts'. If yours doesn't, suggest they consider adding the service. Don't let all of the media hype scare you away from letting your kids use the Internet. These tips, as well as common sense will help you and your children have a fun and safe journey in cyber-space.