On the SANIsoft blog there's a recent post looking at using the Lithium framework with MySQL (the first part of a series).

Lithium is a lightweight, fast, flexible framework for PHP 5.3+. It is still in dev release state but is under active development. This post, as the title suggests, is to introduce you to this new framework using the typical blog tutorial.

They help you clone the latest version of the framework from github, update the default files to change the main page, set up some routing and connect to the database. They include the SQL to create a sample "posts" table and pull some data out of it. There's also some code to help you add, edit and delete posts from the table with Lithium's built-in database layer.