The following video from by Hal Varian, Google's Chief Economist, is a must watch video for anyone who wants to understand how Google decides which ads to display for any given keyword, what order the ads are displayed in, and how much an advertiser pays.
The Auction - Every time someone searches for a keyword, an instantaneous auction occurs among the possible advertisers. Advertisers are initially ranked based on their maximum bid prices for the keyword in question.
Quality Score - Google looks at the historic click-thru rate, ad relevance and landing page relevance to determine a quality score for the possible ads in the auction.
Ad Rank - Google multiples the maximum bids prices by the quality score to determine an Ad Rank for each possible ad in the auction, this rank determines which order the ads will display in.
Final Price - To determine how much the advertiser will pay per click, Google divides the Ad Rank of ad below the current ad (or the minimum price set for the auction of there are now ads lower) and divides that Ad Rank by the current ads Quality Score to determine the actual click price.
The one thing I would have liked to have seen him explain is the Pre-Auction where Google looks at ads with the same display URL to determine which one of those ads will get to compete in the auction. This "pre-auction" actually occurs after Ad Ranks have been assigned, and then all ads with the same display URL are compared to each other, and the ad with the highest Ad Rank get's displayed, and the others get dropped. This insures that the ads with the same display URLs do not affect the Final Price per click paid.
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