Installing the Lejos operating system proved to be straightforward. The steps I followed are repeated here.
First, download the operating system to your local system. You can download the Lejos operating system from http://lejos.sourceforge.net. Just follow the "download" link on the website. As of this writing, you can download files for Linux, Mac OS/X, Solaris, and Windows. The version at this time is 2.1.0.
The download is one Zip file. You can save this Zip file wherever you save temporary files on your system. On my Windows system, I save files like this in a directory named C: \Downloads.
After the download is complete, unpack the Zip file. On my Windows system, I put most of my Java tools under a directory named C: \Java on my system, and this was no different. I extracted the contents of Lejos Zip file to C: \Java \Lejos.
(Note that there are installation notes that may be more accurate and up to date than what I am providing here.)