It 'should' be as simple as removing the ethernet cable from the back of the computer and plugging it into the switch then ethernet from the switch to your pc and xbox.
I'd be tempted to look for a cable router rather than a switch and then even more tempted to get a wireless cable router as this will allow you to use a wireless laptop / nintendo ds / psp or other device (iphone when released).
Decent wireless cable routers can be had for around £40.
Once set-up no cables will need unplugging internet will be available to any device plugged (or wireless) to the router.
You won't go far wrong with one of
these.