Lytro kindly allows everybody get a taste of its technology from Ren Neg's 2006 PhD thesis here. The thesis is titled "Digital Light Field Photography" and explains it in pretty much plain words. I'm not sure if this 5 year old work reflects Lytro's current state, but it's interesting read anyway.
Light field camera from the dissertation:
This appears to be the raw image output (probably after de-mosaicing):
The modified DSLR sensor assembly used in the thesis:
I'd guess it took big big effort to transfer it technology from DSLR with relatively nice sensor output to a modern small pixel sensor with all its artifacts.
Update: Optics.org has a nice article discussion pro and contra of Lytro approach.