You only need a HTTP server like Apache. But you can also use Tomcat, since it handles also requests to static content.

First, download source code of the latest version.
Then, from the README.TXT file it contains, you'll have to:
- download and install last JDK 6,
- download and install Ant,
- run the following Java command in the directory where you uncompressed the archive of the source code:
(keytool is a command of the JDK, if system doesn't recognize keytool, give the full path of keytool or change system PATH)
- run "ant" command in the directory where you uncompressed the archive of the source code. The default javaWebStart target will create signed jars in deploy/lib subdirectory.
- edit deploy/SweetHome3D.jnlp file and change the value of the codebase attribute at line 3 to the URL base where you want to host your version of Sweet Home 3D.
- upload the content of deploy directory on your server in a directory matching this URL base.

Your Java Web Start version of Sweet Home 3D is ready.