The first way to track websites visited by your child is by checking the Internet History. Considering there are more browsers used the steps are different accordingly to each one.
Below I will provide the steps you have to take in order to view the websites visited for each browser in part.

Web pages recently visited on Internet Explorer:

1. Click on “My Computer“
2. Go to your computer’s “C drive“
3. Click on “Documents and Settings“
4. Click on your username
5. Click on “Local Settings“
6. Click on “Temporary Internet Files“

To view recent downloads on Mozilla Firefox:

1. Click on the “Tools” tab (found at the top of your browser after it is open)
2. Click on “Options“
3. Click on “Privacy“
4. Click on “Download History“
5. Click on “View download history“

Websites recently visited on Mozilla Firefox:

1. Press the “CTRL” and “H” keys at the same time.

Websites recently visited on Google Chrome:

1. Click on the “Tools” button and select “History“
2. Press the “CTRL” and “H” keys at the same time
3. Hold down the back or forward button for a couple of seconds (if either button is enabled) and choose “Show Full History” from the pop-up menu that appears

A disadvantage of this easy to apply techniques is that your child can easily clean and delete the Internet History after he stops browsing and you will no more be able to track the websites.

Another method to track websites visited by your child is to use parental control software or web sites monitoring software. When I say websites monitoring software, I don’t refer to keyloggers. Keyloggers are recording chat conversation, application running, keystrokes typed, while a web spy will record only the websites visited. In this way you will not invade the child’s privacy and intimacy. A parental control software has the same functionality like a web spy application and more, can block and filter specific sites. This method should be used if there is a need of a stricter surveillance over children.

The disadvantage is that if you are not explaining to the child the need and the reason why this application was installed, he might feel frustrated and become angry on you.