I'm going to assume that most of you already know about
bitcoins, since they've been known around the interwebs for months, and over the last few weeks have been getting a lot of
media attention. The reason I'm starting this thread is because the value of a single bitcoin (BTC) hit $19.00 yesterday (as of when I first wrote this, now two days ago). Two months ago, each was worth about $1.00. They can be cashed out through any number of exchangers (e.g. Mt. Gox) or used to purchase stuff from a handful of sites that accept it as payment.
Bitcoins are generated in 50 BTC blocks, which are created by running "mining" utilities. These utilities serve to verify bitcoin transactions, meaning that the system is completely decentralized; the currency is regulated and managed by software. The generation of bitcoins is not infinite, though, there is a set number that cannot be passed, and as that number is approached by the generation of blocks by mining utilities, the chance of discovering a block decreases, approaching zero.
Early adopters figured out that GPUs are much more efficient at mining than CPUs. ATI cards especially excel at the task. (My card is nvidia, and mines five to ten times slower than a comparable ATI card.) As a result, there are utilities released that are fairly easy to set up and run to generate bitcoins. There are also groups or pools where many different miners contribute to finding blocks, which are split automatically among the participants according to their contribution. I'm in such a pool, and with my crappy nvidia make five to ten bitcents each day by running the utility in the background.
Bitcoins are sent and received to randomized addresses - using your bitcoin client or 'wallet,' you can generate any amount and use separate ones for each transaction. Wallets are localized to a computer. Computer dies, bitcoins gone. You can always keep them in an online account, like those on the trading sites I mentioned before.
Just generated a new receiving address:
1H5Tx8sNt4EwabCvFX3GAQkzAm8AdGdb7w
Boom. If you opened your wallet, clicked send bitcoins, put that in and an amount, I'd receive some moments later. Beside that, I would see the number of verifications slowly creep up, reaching a certain number before I can actually make use of them, to guarantee that no amount of bitcoins is played with to be counted twice.
If you want to mine bitcoins, the best way to do it is in a pool. Otherwise, anything less than a very powerful rig would take months to find a single block.
This is the one that I use:
http://mining.bitcoin.cz/1. Download the bitcoin wallet software. It is one of the files on the right side of the
main page.
2. Download
GUIMiner. It's the only mining utility that doesn't require you to use command lines to run it, and is fairly intuitive.
Extract and instead of running "poclbm.exe" (which runs the command line version), run "guiminer.exe". If you have OpenCL set up correctly this should launch the GUI. If you get an error about OpenCL, you need to install an OpenCL package from your GPU vendor. For AMD/ATI cards you can get OpenCL here.
3. Sign up on a pool (
slush's pool) and make a new 'worker' on your user page once you've registered and given a wallet address.
4. Change your threshold on your user page to something smaller (mine is 0.2), so that you receive more frequent dispensation.
5. Start up GUIminer and set it up like this:

6. Hit "start mining." Eventually, a rate should appear in the bottom right in terms of hash/s, and your number of contributed shares will climb up on the left.
7. Check your page on the pool site to make sure you are gradually accruing bitcoins.
8.

9. PROFIT!!!
EDIT: No it's not some kind of stupid scam or plot or shady scheme. It's a bit of code invented by a nerd that's a super cool digital currency. <_<