Complete Beginner to Bitcoin? Read CoinDesk’s Information Section to get yourself familiar.
Know about Bitcoin, heard about Bitcoin but still confused how the Math behind it works? Check out a really nice (approx. 2 hour) video course on Bitcoin at Khan Academy.
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So now you know about Bitcoin and want to start owning some? Great! If you’re in the US, by far the easiest and most convenient way is through Coinbase which combines both a wallet service and an exchange where you can buy Bitcoin both at the same time. If you’re not in the US, get an online wallet at blockchain.info or any other wallet service. You can buy Bitcoins on various exchanges depending on where you’re located. Use Google or DuckDuckGo for the conversion between BTC and fiat. See Bitcoinity for BTC/fiat charts.
Crypto-currency Exchanges: There are plenty of other crypto-currencies that can be very good investment/trading plays. To exchange your Bitcoins for altcoins, you can use exchanges like Poloniex and Bittrex. Also, if you want a fairly comprehensive list, check out CoinMarketCap.
Want some free Bitcoins to get started, so you get a feel for things? Check out my Free Bitcoins Guide.
So now you understand Bitcoin and have a wallet and own some Bitcoins. That’s a great start! Start interacting with the community on Bitcointalk Forums.