Shaun Oleson has posted his method (a chunk of code to do it) to connect to the Authorize.NET servers and make a request:

So I've had quite a bit of experience with authorize.NET and PHP and I've found it's difficult to find resources that provide textual examples for integrating the payment processor. I've put together a generic tutorial from documentation that is public. Of course, you will have to specify your Transaction ID and API Login ID. So here you are. If you need assistance or have any questions, feel free to leave a comment.

His example is a large get_auth() function that takes in the credit card information (including billing address) and makes a cURL connection to their servers for the request.

On the GoodPHPTutorials.com website there's a new tutorial showing how to get the Authorize.net API to talk back and forth between it and your application.

I have taken the time to abstract the AIM API into my own class that not only simplifies the code we will need to work with that API but also makes it modular and easy to port from application to application. To begin you will need to download the AuthnetAIM class. You can find it here.

He walks you through the setup and configuration of the library and includes a few examples of how to make both simple and more complex transactions through it.