I did some research before. You can open an account in the exchange to buy it.
eg:
gatecoin - HK based, licensed in HK but the bid/ask is wider. you need to buy bitcoin to buy other currency.
Kraken - quite good exchange which offer full range of crytpocurrency to trade but take long time to open an account
coinbase - biggest exchange in the world but I get issue when I tried to transfer money
On top of, there is bitstamp, quoniex, Poloniex.
Not sure if you study other currency. If you want to trade other cryptocurrency, it is better to check if the exchange can offer that currency and the bid/ask, liquidity.
Like bitstamp, you can trade bitcoin and ripple but cant trade ether
gatecoin, you can trade bitcoin, ether but not ripple. And you need to buy bitcoin to buy ether and bid/ask of bitcoin is wider
Also, i will suggest you to turn on 2 Factor authentication for higher security.
Finally, I got feeling that bitcoin is kind of "water tail" and very risky. Investing other cryptocurrency may have more potential. But please treat it as mark six to buy. Cryptocurrency is still very new concept, too event / policy driven, mkt is not transparent, exchange is not regulated as most of gov does not recognize it as financial product.