I worked at SRI on the CALO project, and built prototypes of the system that was spun off into SIRI. The system uses a simple semantic task model to map language to actions. There is no deep parsing - the model does simple keyword matching and slot filling, and it turns out that with some clever engineering, this is enough to make a very compelling system. It is great to see it launch as a built-in feature on the iPhone.
The NLP approach is based on work at Dejima, an NLP startup: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.5...
A lot of the work is grounded in Adam Cheyer's (CTO of SIRI) work on the Open Agent Architecture: http://www.ai.sri.com/~oaa/
A more recent publication from Adam and Didier Guzzoni on the Active architecture, which is probably the closest you'll come to a public explanation of how SIRI works: https://www.aaai.org/Papers/Symposia/Spring/2007/SS-07-04/SS...