The current version of X-Plane is available from the X-Plane download page, but only as a network installer. For details see the installer description. Older versions are available from a variety of mirror and archive sites. If you can't deal with the download, you can order a CD or DVD. X-Plane.org sells a CD or DVD with updates for several recent versions; see their order page for details. (X-Plane version 8 is distributed on DVD; earlier versions are distributed on CD.)
The mirror and archive sites for X-Plane come and go; the following were known to be available recently:
The X-Plane full download is simply a compressed archive of the X-Plane directory tree. Open it with Stuffit Expander on the Mac; just run it on a PC. Expand it to wherever you have space. On a PC, in the Program Files folder is the recommended location. You'll need upwards of 500MB of HD space for current versions. Plan on several gigs if you want to install the optional scenery.