Id start with browsing around online. A really good book I found based on several recommendations here was "Understanding Exposure" by Peterson. Really good book that gives you the basics and how to use those manual settings on you camera. I think there is another guy (David Bush?) that supposedly puts out some pretty good camera specific books on how to use your DSLR. This should get you started and give you enough to be dangerous.
Those are good places to learn the what I call technical side. The "art" side of things (composition, subject matter, etc) is the harder part. The photo of the day thread here is pretty cool to get good ideas, and you will occasionally see some good critiques and tips (such as the "rule of thirds").
There are probably classes around your local community college too, just depending on your learning style (self taught, instructors, etc)
And then the other leg of this is post production, or in digital terms photoshop/apple's aperature/adobe's lightroom. Again, you can do books (soctt kelby supposedly has some good ones), online tutorials (
http://www.lynda.com is great), or classes. Most would argue getting a decent picture to start with is the key, so this is the last emphasis in my opinion. How much you get into post is really up to you. It seems there are varying opinions on how far to push a picture with post production techniques.
Okay, so Im done rambling - from one new photog to another
Good luck man!