Most Internet browsers offer a "safe search" setting that will filter out a lot of inappropriate content. But they are not perfect: often they can filter out perfectly legitimate sites that your child may want to look at for school research. So, if you want to set the browser to a strict safe-search setting for when you can't monitor, and switch it back for when you can supervise, that might be the best option. Definitely continue to talk to your kid about staying on age-appropriate sites and encourage your child to take responsibility for staying on only those sites that you've said are OK. If you use Internet Explorer, you can find the safe-search setting in the Tools drop-down. In Mozilla Firefox, you can find "add-ons" to download that filter out inappropriate content. You can find the add-ons in Firefox's Tools menu, too.
Information provided by Caroline Knorr, Parenting Editor of Common Sense Media. For more tips about teaching your kids to be safe online, visit Common Sense Media