What you need in Mac OS Runtime for Java (MRJ) which implements the Java Virtual Machine. It comes with the Apple Applet Runner and can be found at http://developer.apple.com/java/download.html
For developing Java software you will need the MRJ Software Development Kit (SDK), which can also be found on the download page. The MRJ SDK comes with "macintoshed" versions of javac, jar, etc. that provide a GUI surface for the usually commandline driven JDK programs. Of course, any commercial IDE will do too, but that wouldn't be free.
Apple also offers a tutorial that describes the creation of a simple slideshow program. Probably a bit more useful is the Mac Java Development Resources page which links to a number of tools (from freeware to commercial products).
A very good source for everything about Java on the Mac is the Outlaw Cafe. It includes a very handy tutorial that helps you set up MRJ, MRJ SDK, and whatever else you need.
One thing that can be a bit annoying is the way the Apple MRJ SDK tools include folders. This can cause problems when your Java classes belong to a package. The easiest way to start javac is to drag the source-code files on the compiler icon. This adds all files into the "Source files" list and the folder that contains them is added to the "Classpath". However, you have to make sure that the classpath lists the folder that contains your package folder (e.g. if the source is "/java/myPackage/MySource.java", then the classpath should contain "/java"). The only way to add that folder is by dragging. Similarly, the "Destination folder" should be the same super-folder that contains the package folder. The path of this folder can by typed in.
When running JBindery, make sure that the Classpath contains the correct folder. (i.e. the folder that contains your package). And if you want to use console input, stdin should be redrected to the Message Window.
There is a decent shareware UML tool that runs native on the Mac. It is called ObjectPlant and can be downloaded from www.macdowload.com