Assuming you have the funds, buying gold coins from the U.S. Treasury is quite straightforward, although strictly speaking you will be buying them from the U.S. Mint, which has been issuing its American Eagle Gold Coins since 1986. These 22 karat coins are available in several sizes and in three formats -- bullion, proof and uncirculated.
Go the American Eagles page of the U.S. Mint website. As of 2011, you will find links to the three formats of gold coins available. Bullion coins are intended for investors, whereas the proof and uncirculated coins receive multiple strikes and special lusters to make them appealing to numismatists. Another key difference is that the U.S. Mint can sell proof and uncirculated coins directly to the public, whereas you have to buy bullion coins from a dealer. If you wish to purchase bullion coins, move to Step 2. If proof or uncirculated coins interest you, then jump to Step 3.
Click on the hyperlink to the American Eagle Bullion coins page. You will find a 'Locate a dealer' icon in the top right corner. This will take you to a database of dealers who sell bullion coins. The coins will still be newly issued from the U.S. Mint, but with the dealer as intermediary.
Follow the hyperlinks for either of the other two options. Click on the 'View Products' icon and you will be taken to a page of available items and a standard checkout system which allows you to pay by credit card. A few simple clicks of the mouse, and you will have bought a gold coin from the U.S. government.