One of the world's most articulate commentators on Peak Oil is Richard Heinberg, who lives right here in Northern California, where he is a fellow of the Post-Carbon Institute.
Here is a video where he explains some of the basics.
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For a much more in-depth look at the issues surrounding peak oil, and a discussion of rebuttals to the idea of peak oil, check out this video presentation on the Post-Peak Living Site. (50 minutes, divided in three parts.)
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If you prefer to read, there is a nice written summary on the excellent Energy Bulletin site here, and another excellent one on the Post-Peak Living site here.
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And here is a telling quotation from petroleum geologist Colin Campbell, founder of the Association for the Study of Peak Oil (ASPO). In a 2006 interview, Dr. Campbell effectively forecasted the 2008 oil spike, which was to be followed by a recession and a subsequent fall in oil prices; a scenario that unfolded exactly as he said:
I think we are facing an oil price shock, 100 or 200 dollars a barrel, an economic recession that cuts demand, and I will not be at all surprised if a fall in demand would make the price collapse again. So we might be back to 20 or 30 dollars a barrel next year perhaps. And so you have a price shock, a recession, a recovery, [which] hits again the falling capacity limit, another price shock. And so I think that in the next few years, we have a sequence of vicious circles and gradually the reality of the situation will filter through. We are on for a very volatile few years with enormous economic consequences.