This is a desciption of how the website of Goodall Memorial Library is currently set up to allow any staff member to edit page contents directly on the site.
First, here is our home page (http://lbgoodall.org):

Staff members who are allowed to edit content of the website are provided with the password and use this page to login as an administrator:

When logged in, the user now sees the home page again, but now it has a set of controls available to the user just above the main content of the page. One of these controls is Edit This Page.

After clicking the Edit button, the user now sees all page content wrapped in an edit box:

Editing the page content is pretty much just like using a word processor, which is well withing the reach of most librarians I have met. No HTML knowledge is required of the user - although for those who want it, the content can be shown in "code view."
This is all made possible by a simple cookie that is set upon login, to identify the visitor as an administrator. This in turn triggers the presentation of the admin controls on each page of the website that has editable content.
The editor is an open source javascript project call TinyMCE. When the Edit button is clicked, TinyMCE is loaded so that the textarea of the page contents may be edited.
When editing is completed, the user clicks on the "save" icon (the top left icon on the editor toolbar), and the revised page content is written to the content file for that page.
The website uses the PHP "include" function to pull content from various files, including the banner/header, left column menu, page contents, and footer.
Simple, elegant, free.
