Download the latest binary zip file (20060719 at the time of this writing) from http://fitnesse.org/FitNesse.DownLoad
Unzip fitnesse20060719.zip to create a folder named "fitnesse"
Run run.sh (Unix) or run.bat (Windows) in the fitnesse folder. This launches a web server on port 80:
FitNesse (20060719) Started... port: 80 root page: fitnesse.wiki.FileSystemPage at ./FitNesseRoot logger: none authenticator: fitnesse.authentication.PromiscuousAuthenticator html page factory: fitnesse.html.HtmlPageFactory page version expiration set to 14 days.
Point your browser at http://localhost