The easiest way to buy from the U.S. Mint is via their Web site, usmint.gov. You can also buy through the toll-free ordering line, 1-800-USA-MINT (872-6468).
The U.S. Mint usually sells only current coins and coin sets, although you can often find the previous year's coins and sets for sale, too. Some of the most popular U.S. Mint offerings include the annual Proof Sets, Uncirculated Coin Sets, bags and rolls of America the Beautiful Quarters, and collector's versions of the American Eagle coins such as Silver Eagles and Gold Eagles. The bullion versions of these coins (meant for investing in the precious metals themselves, rather than the numismatic value of the coins) must be purchased from coin dealers.
Be wary of U.S. Mint lookalikes who advertise their coins in a misleading way, as if they're really the official government mint, releasing new issues direct from government vaults. These companies charge high premiums over the price you'd pay if you bought the coins and sets direct. Several companies are advertising the Presidential Dollars for almost $10 each; you can buy them at face value from the U.S. Mint's Direct Ship Program.