Definitely one of the best things you can do to improve your gaming (after hooking up your Wii to a big screen and using component cables!)
The Wii outputs sound in Dolby Prologic II which will give you 5.1 channel sound. If your surround sound decoder doesn't support DPII, you'll probably get Dolby Prologic sound, which is decoded to 4.0 sound (left, right, center and surround, although your amp will probably do bass management to your subwoofer but let's not get too complicated!)
It's very easy to hook up the Wii to your amp / decoder - simply connect the left/right input on the amp to the left/right output on the Wii.
Then you'll need to select the input source on the Amp to the one you just connected (maybe labeled TV or VCR), and enable Dolby Pro Logic.
If your girlfriend's surround sound amp is part of the DVD player, then it might be more difficult to connect, unless you can find some inputs on the back of it...
Hope this helps!