How does AlphaGo calculate?
Here's the AlphaGo team's paper that has all of the details (behind a paywall): http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html

I gave a couple of tech talks about this recently.
This one is about how AlphaGo works and the match with Fan Hui 2p: https://www.youtube.com/watch?v=HTDxpxmFRGo

I gave another talk last year about why it's hard to create a good Go AI.  This one also briefly explains the rules: http://blog.fogcreek.com/go-and-artificial-intelligence-tech-talk/