You can buy just about any bond through a broker, just as you would a stock. Transaction costs can be much higher than they are for stocks, though.
However, if U.S. Treasurys or TIPS are what you're after, you can (and probably should) buy them directly from the Feds. By doing so, you'll save yourself the fee you'd pay at a bank or a broker. U.S. Treasurys are sold by the federal government at regularly scheduled auctions. For more information, go to the TreasuryDirect Web site.
Getting your bonds through mutual funds is smart for most small investors. The biggest reason is diversification. Because bonds are sold in large units, you might only be able to purchase one or a handful of bonds on your own - but as a bond fund holder you'll own stakes in dozens, perhaps hundreds, of bonds. You'll need about $25,000 to $50,000 to achieve adequate diversification among individual bonds; if you don't have that, then you're better off in a bond mutual fund.
For more, see What's a bond fund?
