Alright, after seeing the back, your fine; however, you do need a receiver like one of the ones in that link I posted. Ok, most subwoofers have a built-in amplifier that will power external speakers, but they are almost obsolete these days. The AC3 inputs on that sub are also obsolete now. It's not a bad thing, it doesn't mean your package is out of date, just that it supports old ways of connecting audio. This package will work fine with a Dolby Digital/DTS surround sound receiver. Sorry to say that cause it means more money, but you'll forget about it when it turns on the first time. You'll need to make sure the receiver you buy has an optical input(most all do now). Looks like you have speaker wire, but you'll need a subwoofer cable(with the price range we're talking, you could just use a nice rca cable).
You connect the speakers to the speaker outputs on the back of the receiver, then the sub cable goes from the receiver's sub output or preout and into the sub's ac3 input(looks to be the red input to the right of "sub" in your picture) After this, you connect the fiber optic cable to the xbox video pack and to the receiver's optical input.
That will get you going. For the speakers you have and my price range guess, you should probably be looking at Sony, Yamaha, Onkyo receivers. All 3 are excellent choices that will suit your needs. You'll probably be good to go with the $199-299 amps. As the main difference between them in this range is output wattage.