How do I install dig?

You can install it by opening a terminal and typing

sudo apt-get install dnsutils

Or via the Ubuntu Software Center by clicking bellow:

For future reference, I found this out by doing a quick search with apt-cache:

apt-cache search dns dig

And then verified with aptitude.

sudo apt-get install dnsutils

To find out which package a file is in you can do

sudo apt-cache search dig

Sometimes that works, but in this case it was useless. You can search for which package a specific file is in using the 'Search the contents of packages' search form here:

http://packages.ubuntu.com/

Another command:

apt-file search /usr/bin/dig

You should install apt-file and update it beforehand:

sudo apt-get install apt-file
sudo apt-file update