Does anyone know the best (and most reliable) way to buy Bitcoin anonymously?
You don't mention where you are located.
One method is to send cash in the mail. http://www.get-bitcoin.com is one merchant that offers that type of exchange. Sending cash in the mail internationally though often has a lesser chance of making it to its intended destination.
There is also the recommendation here to buy using cash via other methods:
There is also the ability to walk into a bank and deposit cash using BitInstant. In most instances, no identity is required. This less anonymous than the other options but probably is adequate.