How It Works
The goal of a Dutch auction is the find the optimal price at which to sell a security.
For example, let's assume Company XYZ wants to sell 10 million shares using a Dutch auction. To participate in a Dutch auction, an investor typically opens an account with Company XYZ's underwriter (usually an investment bank), obtains a prospectus, and obtains an access code or bidder identification code (Dutch auctions often occur online).
During bidding, investors indicate how many shares they're willing to buy and the price they're willing to pay. The underwriter, who acts as the auctioneer, usually starts the auction by offering a prohibitively high price for the security (say, $40 per share in this case). It then lowers the price gradually to say, $36 per share, where two bids come in for 500,000 shares. The underwriter then lowers the price again, this time to $35, and attracts 4,000,000 shares worth of bids. After lowering the price to $34, the underwriter gets another 5,000,000 shares worth of bids; then the underwriter lowers the price to $33 and gets another 3,000,000 in bids before the auction ends.
Below is a table summarizing Company XYZ's Dutch auction:

When the auction closes, the underwriters calculate the highest price at which all shares will be sold. Here, the underwriter wound up with bids for 13 million shares, but the highest bids adding up to 10 million shares are the winning bids in a Dutch auction. The underwriter will then set the price equal to the lowest winning price bid on those 10 million shares (in this case, $34), and all the winning bidders will pay that price. (Dutch auctions are largely handled by computer, and the bids are not compared until the auction time has expired.) Note that this $34 price applies to all bidders, even the ones that bid $36 or $35.