All you do is download the source code, double-click it until it turns into a folder (I'm assuming this post may eventually attract nontechnical or less-technical readers), and then use Terminal to go to its directory. You'll need some Unix-fu to get there, but when you're in that directory, do the following:
sudo make install
And you should be good to go.
I haven't gotten past the next level yet (so to speak), but when I do I'll post a walkthrough.
By the way, if you got Maximum Lego NXT: Building Robots With Java Brains, you may have noticed that the book says lejOS has an OS X build to download on its home page, and you may have wondered how to reconcile that with the fact that lejOS does not have an OS X build to download on its home page, or, apparently, anywhere in the known universe. All I can say is I've been wondering about that too.
In the meantime, installing and compiling the Linux version is your best bet. Even though it isn't hassle-free, compiling Linux software on a Mac is very often possible with only a few steps (less hassle than installing a new video driver under Windows, for example).
Update: this isn't quite accurate. You need
gcj. Haven't installed it yet; will update if/when I get it working.