UPDATE 04/26/2011: If you are installing mod_fastcgi for the purpose of hosting a PHP based application like WordPress, you should consider using PHP-FPM, which is a process spawner and manager for php that is included in PHP 5.3+. Check out my tutorial for installing NGINX, PHPFPM, MySQL, and WordPress.
Problem:
When you attempt to install mod_fastcgi for apache 2.2 on Ubuntu 10.04 using “apt-get install libapache2-mod-fastcgi” you recieve the Error “E: Package libapache2-mod-fastcgi has no installation candidate.”
Solution:
- Add multiverse to lucid main within apt sources:
nano /etc/apt/sources.list
- Add these lines to the bottom of the file:
deb http://archive.ubuntu.com/ubuntu/ lucid main restricted multiverse deb-src http://archive.ubuntu.com/ubuntu lucid main restricted multiverse
- Update apt
apt-get update
- Download mod-fastcgi from newly added repositories
apt-get install libapache2-mod-fastcgi
- Success!

Thanks for this. I've been beating my head for an hour trying to find this answer.
-matt