I'm currently designing a Java application where a Rule engine could be useful. Where is a good place I can learn about how to use them, how they work, how to implement them, see samples, etc.?
The Drools documentation includes a lot of useful, general purpose information. Especially chapter 2, which covers rule engine basics, knowledge representation, etc. It also includes a nice recommended reading list for coming up to speed on rule engines and expert systems.
For most rule engines, a basic understanding of the rete algorithm usually comes in handy for writing efficient rules. I have personally found the Doorenbos paper referenced in the Wikipedia article to be the clearest technical explanation.
Also, here is a list of open source rule engines in Java.
I found this site pretty helpful. Are you looking at building your own, or using a 3rd party library?
You might want to read "Should I use a Rules Engine?" from Martin Fowler's blog.
I have worked on a project where we built our own (very simple) rules engine, with the intention to move to a general rule engine when things got too complicated. Never reached that point though, the system has been running happily with the simple homegrown engine for several years now.