Too much time on the Internet could be unhealthy for children. It's not only up to a parent to monitor what the child is doing online, but what to do if the time is taking away from other activities. It should go without saying, but the first thing a parent can do is just tell the child how much time she can spend on the Internet and enforce that time limit. That should make all other rules unnecessary, but the computers themselves have some elements that can help.
Take advantage of customized control settings. Customized control settings allow you to determine the appropriate time limits for kids, teens and mature teens.
Keep the computer in a public area. Children 10 and under should not need a computer in a bedroom where the parent can't monitor its use.
Use the parental control software options and family tools available on the computer. Set the options so the computer can only be used for a certain amount of time. This is ideal if the children are the only family members using that computer. The programs can be set up so each child can have a specific time allowance per day.
Spend some time with the child when she is on the Internet. This can be a good time to talk with the child about Internet dangers, and how the child should never give out personal information. At some point, ask the child how long she's been online and suggest it's time to do something else.
Find other activities for the child to do. If you are really concerned about the child spending too much time online, get the child involved in sports, theater or some activity around the house.