Here's how to install PostgreSQL and have it run automatically at startup, on an Ubuntu 10.04 virtual machine using Vagrant. This took me a while to figure out:

Add the default lucid32 base box to your vagrant, if you haven't already:

host> vagrant box add lucid32 http://files.vagrantup.com/lucid32.box 

Now make a new lucid32 virtual machine and install postgresql on it: