A number of people have asked me this question, so I’m posting this guide to save myself some typing:

THREE IMPORTANT FACTS ABOUT BITCOIN

1- It’s decentralized. This is important because unlike other attempts at electronic currencies to rival fiat money, there is no business to shut down, no server to confiscate, and no person or small group of people to put in jail. That’s not to say Bitcoin is illegal. It is to say that so far, governments have been pretty good to finding reasons to shut down centralized competition to their currency monopolies (see Egold, Liberty Reserve, Bernard Von Nothaus).

2- It’s open source. There are no secrets in the protocol. A good computer programmer can look at the Bitcoin source code and see exactly how it works. Changes are adopted voluntarily. When a change isn’t backward compatible, there is a long period of debate and consensus building before its adoption. If there exists as-yet-undetected vulnerability in the Bitcoin protocol, it can’t really be exploited without revealing it. The code will then be patched to fix it.

3- Bitcoins are divisible down to eight decimal places — a hundred million parts.

THREE VOCABULARY WORDS

Blockchain – This is the ledger of all Bitcoin transactions. ALL of them. Since bitcoin is decentralized, every user on the Bitcoin network needs to either download the blockchain or have access to a third party service which has downloaded it.

Block – Transactions aren’t written to the ledger one at a time. They are written in groups called Blocks. The network keeps adjusting such that a block will be written every ten minutes.

Bitcoin Mining – A lot of computer do a lot of math which helps ensure bitcoin transactions are honest. As an incentive for people to do this math, the protocol awards new bitcoins to computers which successfully do these math problems. Solving these problems takes the form of a competition. When a problem is solved, a new block is added to the blockchain. The rate of new Bitcoins is predictable and diminishing. The last new bitcoins will be generated in over a hundred years.

GETTING STARTED IN THREE (BIG) STEPS

STEP 1 of 3 – Set up a Bitcoin wallet.

Some (not all) of your choices:

Bitcoin-qt – This the standard wallet which downloads the entire blockchain.

Electrum – This is a light client which connects to a server that stores the blockchain. It has a cool recovery feature if your computer blows up.

Blockchain.info or Coinbase.com – These are web-based wallets. If you’re going to store any significant amount of bitcoins on web-based wallets, enable two-factor authentication. The website will offer instructions on how to do that.

For beginners, I recommend installing Electrum on a laptop or desktop computer. I’m not 100% certain, but if you prefer a mobile device, you may be limited to web-based wallets.

STEP 2 of 3 – Buy Bitcoins.

If you want to just test the waters, the easiest way to do this might be to find a real live person, either an acquaintance or through the Craigs-list-like service Localbitcoins.com. Some people will accept money transfers. Others will want to meet in person. Localbitcoins.com offers a cool escrow service to help.

For people who are either serious or very shy, use an exchange. Here are a few:
Vircurex.com (?)
Coinbase.com (US)
bitstamp.net (european)
bitcoin.de (european)
btc-e.com (Russian) (See What happened to BTC-E)

There are hundreds of them. Most will accept bank transfers. If you don’t want the hassle and expense of bank transfers there are other options.

Some exchanges are starting to accept credit cards. Some Bitcoin ATMs are going online, and other solutions are being developed for in-person cash purchases.

For beginners trying to test the waters, I recommend a friend. If you want to eventually make serious purchases, research exchanges, you’ll have to do so sooner or later.

STEP 3 of 3 – Learn to store your Bitcoins offline before making a serious purchase.

For beginners, I recommend doing this with the electrum client (see below).

FOR THE BITCOIN-QT CLIENT:

1) Make sure your computer is secure and virus free.
2) Install the client.
3) Look at the “receive Bitcoins” tab. Copy and paste those addresses (the long, alphanumeric numbers) into a text file and save it. Alternatively email them to yourself. Share any one of them when you want someone to send Bitcoins to your off-line wallet.
4) Send Bitcoins to those addresses. Confirm that you’ve received them, and close the Bitcoin client.
5) Find a file called ‘bitcoin.dat’ and back it up. You can also follow these steps for creating a paper backup. To simply make and electronic backup, copy the ‘bitcoin.dat’ file to a flashdrive (or to TWO flash drives), and put them in separate safe places.
6) Erase the ‘bitcoin.dat’ file.
7) DO NOT LOSE YOUR BACKUP!!!

To recover bitcoins from offline storage, copy the ‘bitcoin.dat’ file back it where you erased it from and open the client.

FOR THE ELECTRUM CLIENT:
(I recommend this for beginners, because there’s a built-in paper backup feature. There are other solutions, but this is the one I’m familiar with.)

1) Make sure your computer is secure and virus free.
2) Install the client. Make sure you copy down the randomly generated list of words. Put that list of words somewhere safe.
3) Go to the “receive” tab of your client. Copy and paste those addresses (the long, alphanumeric numbers) into a text file and save it. Alternatively email them to yourself. Share any one of them when you want someone to send Bitcoins to your off-line wallet.
4) Find the file named ‘electrum.dat’, and erase it.
5) DO NOT LOSE THE PAPER COPY OF THOSE WORDS!

To recover bitcoins from offline storage, run an Electrum client with a missing ‘electrum.dat’ file. Choose “recover” when it starts. Enter that list of words.

Pro tip: If you want to be super careful in erasing your electronic wallet data, find a tool to securely erase the bitcoin.dat or electrum.dat file. You can also open them in a text editor, edit them aggressively, and save them, prior to erasing.

Good luck!