You don't mine XRP. If you want to transact on the Ripple network you buy it or get someone to give you some for free.
XRP are like the network's tool to convert other currencies and facilitate transactions. They have a value of $0.02 right now, so you need ~$1-$2 worth to get an account and use Ripple.
You can add IOUs of many available currencies (USD, EUR, BTC, etc.) to your Ripple account through a gateway. The funds are held by a gateway (which is like an exchange or bank).
When you add USD to Ripple, what you're really doing is sending USD to your gateway in order for them to provide you with USD IOUs inside of Ripple. Once you have these IOUs, you can move them around Ripple for next to nothing, converting between all available currencies at competitive market rates. See wiki:
https://ripple.com/wiki/Ripple_Introduction
