On the plus side, it's very well documented here.
If you're starting with an existing Ubuntu system, you can skip down to "Setting up Debian for gitian building". This particular section needs a few changes for Ubuntu (it was originally written for Debian 7.4). Specifically, the apt-get line should read:
# that the build script can execute it without providing a password
echo "%sudo ALL=NOPASSWD: /usr/bin/lxc-execute" | sudo tee /etc/sudoers.d/gitian-lxc >/dev/null
sudo chmod 440 /etc/sudoers.d/gitian-lxc
# make sure that USE_LXC is always set when logging in,
# and configure LXC IP addresses
echo 'export USE_LXC=1' >> ~/.profile
echo 'export LXC_GUEST_IP=10.0.3.5' >> ~/.profile
echo 'export GITIAN_HOST_IP=10.0.3.1' >> ~/.profile
echo 'export LXC_BRIDGE=lxcbr0' >> ~/.profile
The rest of this document should work on Ubuntu.
One important note: if you're running this on a fully updated Ubuntu 14.04 system, it won't work due to a bug (see here). I think it should work on most previous releases of Ubuntu, or on an unupdated version of 14.04 (but not 14.04.1), but I'm not certain of this....
(edited several times...)
FYI the bug affecting 14.04 has been fixed in the current version of Gitian, you can use it as the host OS now (but you should continue to use "precise" as the guest OS as per the docs).