There are numerous Bitcoin exchanges available around the internet, but before you go around shopping for the best price to get your digital currency, do remember to first download your bitcoin wallet: bitcoin.org
You can also opt for an easier storage method, by storing it in online wallets, which you can then retrieve without accessing your computer: coinbase.com
Upon that knowledge, you can now proceed to checkout the following bitcoin exchanges:
www.mtgox.com
www.btc-e.com
www.btcchina.com
These are the biggest and most well-known exchanges, and you should probably do business with them for security reasons.