Treasury bills are sold at public auctions every week. The 12-month bill is also known as the 52-week bill. Competitive bids at these auctions determine the interest rate paid on each issue. A group of securities dealers, known as primary dealers, are authorized and obligated to submit competitive tenders at Treasury auctions. Dealers can hold the bills, resell the bills to their clients or trade them with other securities firms. Typically, the New York Fed approves about 20 securities firms to be primary dealers but that number dropped sharply during the 2008 financial crisis as some were merged into other firms or went bankrupt. The Fed has been rebuilding that number regularly and the latest list can be found here. Since these are public auctions, the Treasury must announce the size, date and time of the auction every week. 52-week bills are announced on Thursday for auction the following Monday and issued (settled) on Thursday. If a Monday is a banking holiday, the bills are auctioned on Tuesday. (Department of the Treasury)
Individual investors can participate in Treasury auctions either through a securities dealer (brokerage firm) or via the Treasury Direct program, which saves on brokerage commissions. But brokers commissions are often nominal (especially with discount brokers), and using a broker does eliminate a lot of paper work and other administrative hassles. Brokers facilitate the purchases and sales of Treasuries in the secondary market, which is handy for buying Treasuries at times other than scheduled auctions or for maturities other than those offered by standard new issues.
Interest rates on Treasury securities are determined in the market; the Federal Reserve does not set them. However, bond investors are sensitive to Federal Reserve policy and thus market rates will mirror policy expectations. Usually, bond market players are forward-looking and this means that interest rates on Treasury securities will move in the direction of Fed policy with a lead. As a result, one is more likely to see rising interest rates on Treasury yields during an expansion (and falling yields during economic slowdowns) in advance of policy changes by the Federal Reserve.
Primer on Treasuries
Treasury securities, Treasuries, U.S. government bonds, T-bonds, T-notes, and T-bills all refer to the same type of security: debt obligations of the United States. Maturity refers to the length of the loan to the government. Treasury bills have maturities from four weeks to 52 weeks. Cash management bills (CMBs) are auctioned occasionally, depending on the Treasury's borrowing needs. These are often for short-term needs such as 12 to 14 days. Since 2008, the Treasury ruled that all securities it issues now have minimum denominations of $100 and must be purchased in increments of $100.
How bills work
Since they mature so quickly, bills are simply sold at a discount to their face value at maturity. The interest is the difference between the purchase price of the security and what the Treasury pays at maturity. For example, if you bought a 3-month bill for $9,800 and received $10,000 at maturity, the interest payment would be $200.
Treasuries offer a measure of security unmatched by other investments - the U.S. government guarantees the initial investment (the principal) and interest payments. When Treasuries are resold in the secondary market, their prices are often significantly different than their face value since prices in the secondary market fluctuate based on the economic environment, inflation expectations, Federal Reserve policy, and simple forces of supply and demand.