The basic search tools of Google and Yahoo are two of the most popular, simple and straightforward "search engines" to help you find websites. With Practice you will become adept at choosing appropriate key words.
The BBC's new computer course for basic users. Click your way through the stages, learn how to control the mouse and keyboard and other basic functions. Very clear, presented as short videos and some simple games.
More of the BBC's new computer courses. This one is about basic internet uses, and takes you  from how to search, including some of the confusing issues like registering and choosing passwords to   email and shopping on-line.  Short videos.
Yet more of the BBC's computer courses.  A basic introduction explaining the social networking websites (such as Facebook and Twitter).  How to get started, stay safe and protect your privacy.
Simplicity Computers.
A very clear and simple site about the 'Simplicity Computer', a unique, purpose built computer for the older user, presented by Valerie Singleton.  See what it looks like and how it works.
A clearly presented, online tutorial to help you learn how to touch  type. Look for the links down the  left hand side that says  Keyboard Lessons to get started. NB some small ads appear on the pages which are not tutorials. 
AbilityNet's very clear site that helps you customise your computer to suit your needs. Practical help with things like making text easier to see and making the mouse easier to use.  Especially good for the elderly computer user.
A comprehensive and attractive  guide to broadband and what it means, who the providers are, and what people say about the providers, how to get started and a useful jargon buster. A good reference tool if you are thinking about getting  broadband.
Excellent comprehensive guide to protecting your computer from all kinds of threats and safe online shopping and banking. Tells you what to do, why and how. Answers lots of worries about online safety.

Microsoft's comprehensive guide to online security.  Quite technical, but gives advice on all aspects of computer protection for you and your family online. Very thorough and clear. Deals with all the main issues including email scams and passwords.