Selling your spare GPU time
So what is Bitcoin? If you follow the link above you'll see a video created by some very smart people, but basically it's a decentralized currency (I'm not saying "electronic" because they all are, in a way). It can fully self-regulate: policy decisions are only made by a 100% community vote (it's an open source project), the supply is fixed algorithmically so no inflation can be introduced and transactions are confirmed by a majority vote from miners.
To get a wallet you'd normally use the official bitcoin client, but it has to download the entire transaction history, which can take days. That's why, after careful consideration, I choose to go with an online wallet from Blockchain.info - their advantage is that all encryption is performed in your browser, so everything that is ever stored on their servers is encrypted with a key only you have. The obvious disadvantage is that there's no help if you forget your password, because they can't access and restore your data, but neither can hackers. Of course, if you have a virus on your computer that can modify the memory of your browser, it can do anything you can.
You can generate a wallet offline, so you can have a computer that was never connected to the Internet generate a private key which you can then print on a piece of paper and store in your safe. This way the funds you send to that address can only be spent by physically opening the safe. This is only possible because Bitcoin doesn't require registration, there is no central authority to which communication must be initiated.
The miners are just regular people that run mining software on their computers, verifying transactions by completing difficult calculations. The key here is that the calculations are so hard and run on so many computers that any single entity isn't capable of creating a verified fake transaction - it will have to be faster than the entire network (so it has at least 50% of the total computing power).
To mine you'll need a relatively recent ATI graphics card. For some reason, Nvidia cards are extremely inefficient at mining, so you won't be able to cover your electricity costs. Specialized hardware is available, but currently there's much talk about a next generation of chips comming, namely ASICs, so for now I'm using my Radeon HD 7770 with GUIMiner. I'm mining on Slush's pool. You don't need the Bitcoin client and the chain - you just configure GUIMiner to connect directly to the pool (everything you need to do is described on their homepage) and start receiving and completing tasks.
A pool provides a smaller, but constant reward, while mining solo on the current difficulty means it could take months until you get the 25 BTC. The way pools work is by handing out easier challenges, and giving you shares from the reward for each one you solve. Eventually, some of these easier solutions will also meet the stronger requirements of the Bitcoin network, thus receiving a 25 BTC reward, which is then split accordingly between participants. When you reach a minimum amount (the lowest setting is 0.05 BTC), it is sent to the address you have provided (e.g. your wallet address from Blockchain.info).
So this is the way I generated around 0.09 BTC for a couple of days during December (the cool thing is the energy is not really lost, it heats your room). Then, 1 BTC was around $15. Now, the 4th of March, the price of 1 Bitcoin is already over $120. This suddenly meant I have enough money to buy my domain name, which is possible because Namecheap works with BitPay to accept Bitcoin payments. They had a great promotion, so I sent the 0.041 coins to the address they requested, got a confirmation after some time (maybe half an hour, I'm not sure) and purchased the domain. What BitPay does is that they make it easy to accept BTC, they handle the payment for you and send you your preferred conventional currency to your bank account. This way all accounting is done the usual way, you can pay taxes, etc.
So this is the story of how I got my domain name. I hope you're now as excited about the future of Bitcoin as I am - with organizations like Namecheap, Reddit, WordPress and many more standing behind it, the future sure looks bright.