Safety By Age
2 to about 4:
This is the age of "lapware," when children start interacting with the computer in the presence of a parent or sibling. There are numerous activities and sites that are likely to be appropriate for this age group but, in most cases, it makes sense for the parent and child to be exploring together. This is not just a safety issue, but also a way to assure that the child has a pleasant experience, and to help build bonds between the child and the older person who is surfing the Internet with them.
Starting at about age 3, some children can benefit by having a bit more independence so that they can explore, experience discoveries, and make mistakes on their own. That doesn't mean that they should be given free access. It's probably best for parents to choose the Web sites they visit and not let them leave those sites on their own. You don't necessarily need to stand over them or sit with them the entire time that they're in a known safe site.