This is a question many people ask when they're introduced to Bitcoin.
Bitcoin sounds interesting, but if I want to use this system I will need to get some coins, otherwise, there's no way I can spend them! How can I start?
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You can use an online exchange such as BitStamp for US dollars, as well as many others for dollars, and other currencies.
See the wiki for a full list of ways to buy bitcoins.
Brokerage services allow you to buy or sell directly from them instead of relying on a third party to offer the trade with the exchange just taking a cut. One such service is Coinbase.
You can use tools such as localbitcoins.com to find people near you who will trade cash for bitcoins. (Note, however, that localbitcoins strongly encourages you to use their service despite the fact bitcoin does not require using a 3rd party to do in person transactions)
Mining bitcoins is very technical, and not for many people. Unless you already have the hardware and technical skill to set it up I would not recommend mining as a way to get bitcoins.
I believe by far the best way to get bitcoins is to provide goods and services for bitcoin. This stimulates the bitcoin economy which in turn makes the bitcoins you receive more valuable.
Basically there are five main ways of getting bitcoins:
first of all I have to warn that currently there is almost impossible to mine by your own. You need to have a dedicated hardware (you can see hashrate comparison here) which is really costly. Even with this dedicated software it is really a small chance (current total hashrate is > 850 Thash/s) that you will create a block.
So most probably you have to mine as a part of the pool. There are quite a lot of mining pools available, but mostly you would like to join some big pool to have a high percentage of guaranteed small payoff. Pools hashrate distribution you can find here. I by myself have tried to mine on two different mining pools : BTC Guild and bitMinter. Just my own opinion, that it is easier to start with bitminter, because they provide you with easy to use software for mining and detailed instruction.
One last word of warning: most probably if you will start mining right now with your GPU, you will spend more money on electricity than you will gain from mining. But if you are going to do this just for curiosity, it might give you some micro part of a bitcoin.
As with mining, you have plenty of options as well. The only problem is that right now you are dealing with your own real money. So you have to be careful what to select. At some period of time there were a lot of fake bitcoins selling sites, so if I were you, I would rather go with bullet proof places:
It is also possible to find local trading partners through services such as localbitcoins.com or at Bitcoin meetups.
If you already have a shop or are planning to start selling something in the near future, it is pretty easy to accept Bitcoin as payment, in fact easier than to accept Credit Cards for example. If you are worried about Bitcoin's volatility, there are different payment processors, which will convert your Bitcoin payments into your national fiat currency for a fee, usually lower than Credit Card Companies. – You can opt to keep a percentage in Bitcoin.
Not surprisingly, but there is a lot of web-sites, where you can get bitcoins for free. Do not be overexcited by this - you can not make a fortune out of this :-). Most probably they will give you 0.000001 bitcoin for free. On most of such websites you have to watch some stuff or to other useless things. So you are exchanging your time for micro payment. In my own question on bitcoin beta, there is a list of many of such places. If you know any other place - feel free to add it.
Try to ask your high tech friend. There is a high chance that he already knows about bitcoin and may be have a couple of coins. He might give you a small micropayment just to try. But do not try to abuse this: there is no point of asking people in places like this to give you 0.00001 bitcoin.
This is from my answer on Money.SE:
You can set up your computer to mine for Bitcoins, you can exchange goods and services for Bitcoins, or you can purchase Bitcoins on an exchange. Some people will trade their programming or web design services for Bitcoins; others sell goods like alpaca socks in exchange for Bitcoins. The exchanges operate similarly to forex in that someone can trade say USD for Bitcoins (instead of trading USD for Euros or British pounds). According to Bitcoin Charts, the Mt. Gox exchange has by far the highest volume, but in recent months Trade Hill has gained some ground.
As for mining, computer performance matters as well as the "difficulty." The difficulty in mining fluctuates so that it becomes harder as the collective mining power increases. Mining is set up so that someone earns a block of 50 Bitcoins on average several times an hour (but this reward will decrease with time such that only 21 million are ever created). You can't ever make progress towards mining a block of 50; mining is an inherently random process. It's possible to successfully mine two blocks in short succession only to have a huge gap before successfully mining another block.
I should note that CPU mining is essentially pointless right now. On average it would take several years even for top-end CPUs to successfully mine a block. GPU mining (where the processor built into graphics cards is used) is what is popular now. Even so, it would take on average a long time to generate a block even with several GPUs. As such, many miners join mining pools where everyone shares credit when anyone successfully mines a block. This serves to decrease the variance and is will lead to a more regular flow of Bitcoins instead of long gaps followed by blocks of 50.
You can buy or sell bitcoins by connecting any U.S. bank account on Coinbase.com
All of the below is now obsolete. I keep this answer in place to show the ongoing changing nature of "Bitcoinland".
In the UK I used Britcoin.co.uk
It's run by an established member of the Bitcoin forums (genjix). Trading is very light in comparison to the other exchanges, but it does accept GBP via direct bank transfer.
Of course the best way to obtain Bitcoins is to earn them in exchange for goods and services. Perhaps by offering your skills on forbitcoin.com
Miners are the main source of Bitcoins and if you are looking for high amounts you should definitely contact them, but in most cases, they have exchangers they are working with.
They are getting bitcoins from miners or people and offering it to traders. I'm using coinify which is easy, and you can pay using your credit card (Europe) and localbitcoins.com is also good for trading bitcoins regardless the high fees.