I saw Ed Begley Jr. and Bill Nye talk about it.
Anyway, you can see our filthy panels above. That is after five months on the roof.
I chose the laziest method of cleaning possible and just sprayed the panels with water, which seemed to work great.
The cleaning had a measurable impact on the production of the panels. The graph below shows two days before cleaning and two days after cleaning. The panels are producing about one more kWh per day after being cleaned.