How do I restrict browsing to just a specific list of websites?

Click the Menu button
Then Parental Control menu item
To add the current website to the allowed list, click the + button to left of Add current site

OR

To add another website to the allowed list, enter the website in the Enter site textbox then click the + button to left
After enter all the websites you want to browsable, click the Restrict browsing to only these websites:
Any attempt to access a website outside the list you specified, will result in a dialog similar to the on below. Any of the listed websites can be accessed directly by clicking the button the left of the website