The power of the Web is in its universality. Access by everyone regardless of disability is an essential aspect.
- Tim Berners-Lee, W3C Director and inventor of the World Wide Web
Accessible web design is simply good web design. It means that your pages will be able to be viewed most easily by everyone - regardless of their browser (do they use IE or Netscape or something else?), their screen resolution (not everyone uses 800x600), their personal preferences (often people prefer to see the text alternative to pictures which take a long time to download), and even their disability (some might be using software that speaks everything back to them).
There is a huge amount of information out there on good web design. The best source is from the founding fathers of accessible web design - the World Wide Web Consortium (W3C) - who have put together the guidelines that have been adopted globally as the benchmark to which all forward-thinking web authors ensure their pages comply. You can find the Web Accessibility Initiative (WIA) home page at www.w3c.org/wai.
If you have existing code you would like to test for its accessibility why not ask a policeman? You can always trust a good old English Bobby. A good utility for identifying those parts of your pages that transgress good practice can be found at bobby.watchfire.com. A policeman's helmet will appear next to each guilty offender.
A good way to test for accessibility is to look at your web page with a text-only web browser such as Lynx, Links, Elinks or W3M. If you can make sense of your web page with such a browser then someone using a voice-reader will have a fighting chance.
You should also try to use HTML/XHTML and CSS that is written to W3C web standards so that your web pages will be usable by any standards-compliant browser. You can test your web pages using the W3C HTML and WC3 CSS validators.