How can I safely upgrade an Ubuntu installation from one release to another? What should I do before upgrading to ensure it goes smoothly, and is there any clean-up I need to do afterwards?

In particular, do I need to do anything special if I am using packages from PPAs, if I have a graphics card that needs drivers, or if I'm running a custom Linux kernel?

This is a general question , but as example we take Ubuntu 12.04 and Ubuntu 12.10