1. Open an account on any Bitcoin exchange (mtgox.com, bitcoinusa.com, etc)

2. Fund your account by wire or ACH transfer (supported by most exchanges)

3. Place a 'buy' order in 2 mouse clicks to buy BTC at the current market rate. Done.

Or if you know someone in the real world who has coins, just make him a cash offer to send you directly the BTC (using the Bitcoin software, without going through a third party such as an exchange).

There's also #Bitcoin-OTC where trading is done over IRC. Here's the Order Book, viewing USD offers: http://bitcoin-otc.com/vieworderbook.php?sortby=price&so...

For small amount of bitcoin, you can use CoinPal at http://coinpal.ndrix.com/

Even though I did not personally used it, many people recommend the service.