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.