<p>I need some basic CMS functionality with rich text editing. On stack overflow there is a regular textarea edit control, with support for Markdown style syntax formatting. That would be beyond my users, so I want something like a rich edit control that you can type into on the web site. I know it is possible, as loads of sites do it, but I don't know where to start.</p>

TinyMCE
is probably one of the more popular versions of this sort of thing. You can customize it to fit your needs, in terms of what functionality you want to offer your viewers. a few alternatives (tend to be lighter weight than a full TinyMCE install):
FCKeditor
Xinha