Checking Browser history is one of the first steps to keeping track of where your children are are surfing on the net. You will first need to configure your browser to begin logging the history. 

In Mozilla Firefox

You get this box by going to the tools tab at the top then selecting options. In options select the "Privacy" tab. as above. Check the options that you would like to see, make sure you keep history long enough for you to check it, but it does consume storage space. So if the computer is heavily used you may not want to hold everything around. Checking Mozilla's history is easy! Just press the keys Ctrl + H, so hold down the Control and H key together and the history browser comes up.

In Google Chrome

The default setting in Chrome is to log history, so all Chrome users must do is hold the keys: Ctrl + H, to bring the visited sites list up.

Notice how easy it is to delete the history, if you suspect this is happening to hide things, you should consider installing a third party application. Read more about that below.  

In Microsoft Internet Explorer

To configure the logging settings in Internet Explorer, go to the "Tools" tab, then select internet options. That will bring up this window:

Then in "Browsing History," select settings:

At the bottom of this new window is the number of days the history is held in memory, change this if needed. Once again to check the history after it has been configured press the ctrl + H keys and it will pop up.

Now, after seeing how easy it is to manupulate these settings. You may want to install a third party parental control application. Some of these programs will require a password to be able to make changes in what is logged.

http://www.safefamilies.org/ may be a good free solution.

http://www.webwatchernow.com/ is a great program! It isn't free, but it's easy to use, and completely undetectable. It also can be monitored from the internet, so you don't have to keep checking the actual computer (maybe it's your childs computer and you don't want them to know you're checking.) Another solution may be a simple Keylogger. These small applications simply log every key stroke. So everything that is typed into the computer is preserved in a log that you can view later. You can download those from http://softpedia.com/ .

If you have any questions please leave a comment.