Guide on switching from distro-provided nginx to nginx built from source?

[Jeff Kaufman]

I haven't been able to find a good guide for people who have been
using nginx as installed by their linux distribution who want to
switch to using an nginx they built themselves.  This comes up a lot
with ngx_pagespeed because for many users we're the first module they
want which isn't packaged with their distro.  Does this guide exist?
If not, I might write one for ubuntu at least.

This is somewhat similar to a regular "install nginx from source"
guide but it needs to have at least:

* how to get a list of the modules you need to add (nginx -V | grep
configure_arguments)
* how to copy your config over
* how to keep and modify your nginx init script when uninstalling the
distro-provided nginx
* how to do all of this with minimal downtime and risk on a single VPS

Jeff