I just spent some time writing up an email to a friend to introduce them to Bitcoin. I figure I might as well share it:
As promised, here's a link to get you started: https://blockchain.info/wallet/new
Pick a strong passphrase with multiple words and some random numbers at the end. You can't recover it if you lose it or forget it so write it down and keep it safe.
Once you've created a wallet, send me your bitcoin "address" and I'll send you a small payment.
People all over the world are starting to use bitcoins as a global currency because it's independent from governments, banks, and corporations. It runs on a voluntary peer-to-peer network that anyone can participate in by downloading and running the free bitcoin software from bitcoin.org/en/download. I don't recommend installing that though, instead just use the blockchain website I linked to above which runs the software on your behalf and allows you to access your account from anywhere that has Internet, including your phone.
If you *were* to run the full software though, it would cause your computer to connect up with other computers running the software to relay and validate transactions and generate new bitcoins. 25 new bitcoins are generated every 10 minutes and distributed to all the computers in the network in proportion to how much computing power they contributed during those past 10 minutes. This keeps the supply of bitcoins stable and scarce so they can't be created or inflated arbitrarily (unlike dollars). 12 million bitcoins have been generated so far since the software was first released in 2009 and only 21 million will ever exist. Each bitcoin can be split into 100,000,000 smaller units called "satoshis" so even a single coin could run an entire economy.
One bitcoin sells for about $330 CAD right now. You can see what they're trading for at any given time on different exchanges around the world at bitcoincharts.com/markets
Payments from one bitcoin address to another cost just a couple of cents no matter how much or little you send and as you saw registering for an account is free and doesn't require you to identify yourself. That means you can accept payments from anywhere in the world or send money to anyone for free and your account can't be monitored, frozen, or confiscated by the government or banks. This lets you take your money with you anywhere in the world as long as you remember your password. Revolutionary?
That's probably enough to get you started but do some more reading on it at bitcoin.org and let me know if you have questions. If you decide you want to buy some bitcoins let me know and I'll be happy to sell you some. I bought $500 worth back in 2011 when they were selling for $5 each so I've made a 6600% return on my investment. I can't promise that it'll continue to grow that fast of course but I don't see any reason why it wouldn't as long as more people keep learning about it and using it.