Once you've tapped the Install button, you'll be taken back to the home screen of your device, just like you're installing an app from the App Store. In this case, though, the app that is being installed is Cydia, the alternative app store.
Over WiFi, this should take a few seconds. Over 3G, it will take a little longer.
Look for the Cydia icon. When you see it and can click it, your device is jailbroken. Believe it or not, it's that easy!