Please see http://wiki.nginx.org/Main for more information. See http://arstechnica.com/gadgets/2012/11/how-to-set-up-a-safe-and-secure-web-server/ for a tutorial on how to install Nginx.
To install, you can install the version which is in the standard Ubuntu repositories but it is normally quite old and will not have the latest security patches. The best way is to update the repositories first:
apt-get update
apt-get install python-software-properties
apt-get upgrade