Your broker at a major bank is the only place where you'd be able to buy a new offering of bonds. There's usually some minimum quantity you have to buy, in the range of $30k-$100k minimum. You basically have to ask said broker to tell you when they're available. (give you the list of new issues periodically)

I think you can buy existing bonds on the market through more normal channels including discount brokerages.

edit: Public Service Announcement - don't trade in bonds, because you're virtually guaranteed to get taken advantage of hardcore by Wall Street bond traders, even the "flow traders" that do the transaction for you. One example is the broker giving you a price (via the trader) that reflects the bank's own book instead of the actual open bond market (you can check the discrepancy by demanding to see the Bloomberg data on the security). The bond market is still even to this day nothing like the stock market. Visibility & transparency (in the stock market) are your friend.