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