IMO, this graphic (from a presentation by Sadad Al Husseini, the retired head of E&P at Saudi Aramco) is really all you need to see to understand peak oil. The bottom line is that there is a point around 105-110mbpd where you just can't meaningfully increase oil production no matter how much people are willing to pay for oil.
The solution for the US (don't know about China, India, etc.) is actually really simple: heavily tax gasoline and use the proceeds to subsidize more fuel efficient vehicles until we have completely turned over our vehicle fleet from a 20mpg fleet to a 60mpg fleet. It should take about 10-15years and doesn't require any new technology: just make cars smaller, lighter and slower and then drive them less.