Here’s a nice primer on Bitcoin from BoingBoing:

Bitcoin is a peer-to-peer network, a set of protocols (standards for interoperability), client interfaces (called wallets) and a currency that operates on top of all of those technologies. The bitcoin system allows any person to send or receive a fraction of a bitcoin (the currency unit) to another person, anywhere in the world. The bitcoin system operates on the Internet without the need for banks or bank accounts and allows people to send money like they send email.

To start using bitcoin, you need a bitcoin client, or “wallet” application. The bitcoin client allows you to use the bitcoin network, just like a web browser allows you to use the web. There are many different types and makers of bitcoin wallets, for desktop and mobile operating systems and also available as web applications. To receive bitcoin, you need a bitcoin “address”, which is a bit like an email address or bank account number. If someone knows your bitcoin address, they can send you money, but cannot do anything more, not even identify who you are or where you are. Therefore, you can freely share your bitcoin addresses with anyone without fear or security risk. Once you have a “wallet,” it can create any number of bitcoin addresses for you, even one per transaction. Give those addresses to anyone you want to send you bitcoin. Tip: bitcoin addresses are created by your wallet and do not need to be registered with anyone, or linked to your identity or email address. They can be used immediately to receive money from anyone and become part of the network once they have some bitcoin sent to them. Bitcoin addresses always start with the number “1” and they look like a long string of number. One of my bitcoin addresses is “1andreas3batLhQa2FawWjeyjCqyBzypd”. This is known as a vanity address, because it has my name in the beginning, but it works just the same as if it was a long string of random letters and numbers. I use it to receive tips and donations from people all around the world.

The remainder of the article explains the entire process, including how to pay for things using bitcoins, tips on securing your bitcoin keys, how to find vendors that accept bitcoins, etc.