This post from Tech Soup is a good, brief introduction to the use of databases in your organization.

The author of this article (a nice techie from ONE/Northwest) finds that you should really call in the professional to get things set up — I would agree, but don’t let that keep you from learning how to use it.

A database is an investment of time that can really pay off, especially if you have been managing your donor lists, inventory, etc. by hand. But that means you need to know how to use it.

Make sure to check the entire selection of articles about nonprofit databases at Tech Soup.

Here’s a bit from the overview:

While it’s no simple task, developing a basic Web site made up of pages of text and images is usually a job that can be taken on by the staff of a nonprofit organization, hopefully with a little help from a professional designer who can aid in the development of the site’s look and feel. Implementing advanced features on your site, however, will most likely require a level of expertise that doesn’t make sense for your organization to internalize. The goal of this article is to explain the benefits of database-driven Web pages as well as the possibilities and vocabulary involved to help you make informed decisions.

The best book I have found on Access 2003 (The current most popular database software) is “Access 2003 Personal Trainer” from O’Reilly (a reliable publisher of training manuals.) This book represents their newest approach to teaching computer materials at a normal-people level.

I appreciate it’s informal (superhero) style, it’s clarity of writing (though there are still a few proofreading errors in the text, the thoughtfulness of the writing — the book is much more than a simple, huge, frustrating dictionary of specs that you so often end up with.
In short, it’s a real text that can get you into using Access for the first time. The best part: it comes with a tutorial cd that is actually useful. Not merely a appendix of sample databases, it provides a quick shot-in-the arm approach to doing specific tasks.
If it gets too easy, just quick through. The only thing I with it had was a detailed walk-through of creating and using a simple database.