I am starting a new web application in PHP and this time around I want to create something that people can extend by using a plugin interface.
How does one go about
Good advice is to look how other projects have done it. Many call for having plugins installed and their "name" registered for services (like wordpress does) so you have "points" in your code where you call a function that identifies registered listeners and executes them. A standard OO design patter is the Observer Pattern, which would be a good option to implement in a truly object oriented PHP system.
The Zend Framework makes use of many hooking methods, and is very nicely architected. That would be a good system to look at.