I have a general old-fashioned phone that has no special app system and uses Java (I assume ME) for the few applications you can use on it.
This is still a decent userbase and I'd like to start programming for this type of phone. I already know basic Java theory and syntax, so.. where do I get started for programming for non-smartphones?
I would start with a book on J2ME and work from there.
Try Beginning J2ME: From Novice to Professional.
You could also download the J2ME SDK and play around with the example they give.
For tutorials have a look at the stackoverflow question http://stackoverflow.com/questions/584923/do-you-know-a-good-j2me-tutorial as mention in my comment.
I started with writing simple Flashlight application (choose how much seconds screen will remain lit) in NetBeans ME. And other app which I mange was Countdown with some graphics and sound. After that I found limitations too much annoying and now I'm waiting for my Android phone.
in short: If you want to try it out - you don't need to buy books. There are plenty of tutorials around. But, if you want to start deep development - don't waste time.
Best programming environment for Java ME IMO is Eclipse with EclipseME. Includes lots of built-in stuff about packaging your midlets etc. The SonyEricsson wireless toolkit is great for PC-based testing and debugging, but don't forget on-device testing!
If you don't know much about Java ME's lifecycle, then get reading as widely as you can, and try lots and lots of examples. Start with the JSR-118 (MIDP2) javadocs; you'll want these open on your desktop at all times while coding.
Don't waste too much time with the form-based user-interface; I recommend either rolling your own using Canvas, or read about LWUIT.
You can do all sorts in Java ME and target a very broad range of handsets. HTTP capability is guaranteed, so you can hook up to a public web service, or create your own using something like Google Appengine.
Finally, you can release your app very easily on somewhere like Get Jar. Don't be put off by those who say "no owners of Java ME handsets want apps", you'll find the most popular user bases on this site will be users in countries such as India and Indonesia.
Good luck!