An excellent place to start would be the official documentation for integrating with Dynamics AX 2012 found here.
A tool that you might want to use is the Application Integration Framework (AIF services). You can either integrate with out of the box services developed by Microsoft, or create your own services. This will require knowledge of AX and X++. You could then expose and call these services from your PHP application. To begin with AIF, go here for the main page, which has architectural and planning documentation and here for a more specific documentation on (document) service development. For exposing these services via what are called "adapters", look at the links at the top of this page. You may be interested in the HTTP adapter for example, to expose your service in that manner.
Another option could be to create your own services in PHP and call them from AX. You could call the services from X++, but due to the limitations of the language this is sometimes easier achieved by calling the services you created in PHP from a C# library. The C# library would use proxy classes to call X++ objects to read/write whatever data you are getting/posting to/from your PHP services. This and this may be interesting starting points for documentation on how to do that.
Getting the know the Dynamics AX specific terminology by reading these docs can help with your google-fu later on during development... but once you get a feel for the terms there is a lot more info on forums and whatnot that you'll be able to find.