The answers vary depending on what kind of thing you're building.
If you're building a library, it's best to distribute your work as a jar file. It's possible to refer to your jar dependencies via the Class-path attribute in your jar manifest, although I generally think that's uncool. That attribute was designed for applets and it's used infrequently enough in libs that when this technique pulls stuff into the classpath (particularly common stuff the user might already be using), you can get unexpected version conflicts. And it's hard to track down why you're seeing them.
Publishing a jar to a Maven repo with pom info to track dependencies is an excellent choice for libraries as well. If you do that, please publish your Maven coordinates in your docs!
If you're building an app, the two popular choices are to distribute a zip/tar/whatever of a deployment structure OR to use an installer program. If the program is a server-ish kind of thing, the former is far more common. The latter is more common for clients. Generally, the installer program is just going to lay out the deployment structure and maybe do some extra tasks like installing in OS-specific locations.
To build your deployment structure (aka "kit") you'll want to create a repeatable process in whatever build system you're using. Ant has copious examples of this and Maven has the assembly plugins that can help. Generally you'll want to include a jar of your code, any dependencies, scripts to start the program, maybe a JRE, and any other resources you might need.
If you want to create an installer, there are many options both free and commercial. Some folks I know have recently had good experiences with the free IzPack but check out your options.