You generally can buy bonds through a full service or discount broker and some banks and credit unions. You can also buy US government bonds directly from the U.S. Bureau of the Public Debt Web site (www.publicdebt.treas.gov/). If you buy bonds on their web site you can pay by credit card or debit card.
Another option is to buy mutual funds specializing in bonds. Almost all the large mutual fund companies offer several funds based on bonds. A bond mutual fund provides the benefits of being diversified in many bonds.