I was having trouble myself finding any fully working examples of the Method API in PHP or, better yet, a PHP example that was integrating data from a WordPress Gravity Forms form into the API call. I've figured it out and thought I'd post in case others found themselve in a similar situation.
I ended up using nusoap: http://sourceforge.net/projects/nusoap/
In my situation, I have a form on a WordPress site using a Gravity Forms form. I wanted to continue using the GF functionality, but to also submit directly to my client's Method account. I am not sure if this is the case for everyone, but for new customer leads I needed to insert an entry in the Customer table as well as the Contacts table. The unique identifier for both is the full name (or "Name" in my example).
You can find my code here: https://gist.github.com/relish27/67432c710f4b4904ca6f