It's complexity is not due to it's methodology, but rather it's subject matter. Prayer deals with God, and anything that puts us in contact with a being who, by definition is ineffable, will naturally be somewhat opaque as well.
Here is a video I made where I open up the conversation about the question "what is prayer?"
It's not the last word on the subject and I would love to hear from you.
If you are interested in further resources about answering the question "What is Prayer?" here are a few:
- If you want to hear more about the Atheist Prayer Challenge I reference in the video you can go to http://www.premier.org.uk/atheistprayerexperiment
- Another article about non-believers praying can be found here http://bit.ly/atheistprayers
- A nice little overview from a Catholic Perspective: http://catholicism.about.com/od/prayers/f/What_Is_Prayer.htm
- Here is a nice collection of thoughts from people on why they pray: http://storify.com/tonyjones/why-pray