Easier way, with perhaps a fee slightly larger than what the other poster described. Go to coinbase.com Buy bitcoin. There's a limit on the amount that you can buy and have available immediately, anything more than that will be available in a week, but will keep how ever many you buy based on the Current exchange ratio.
After you do that, you need to make an account on an exchange, poloniex is the one with the highest volume, but it's been lagging due to said volume lately /shrug, and you'll use the send function from coinbase to send to your digital address on whatever exchange you pick. It'll be a long string of numbers / letters. And be sure that you're picking the correct coin's deposit address that you're using.