Far Left (red X) - This is your present wireless network connectivity. If a red X is displayed it indicates that you are currently disconnected from your wireless network. If you were connected you would see signal bars similar to cellular connectivity bars that you would see on your cell phone.
Second from the left (arrows) - This I'm fairly certain is the ActiveSync icon. This indicates that you currently have the device in the cradle and it has an active ActiveSync connection to your PC. This would potentially explain why it appears that you have no internet connectivity. If the device is in the cradle the wireless network connectivity is often shut down.
Second from the right (battery) - This is a fairly obvious icon as it resembles a battery, indicating how much charge is left on the device. You may notice a small lightning bolt superimposed on top of the battery icon. This indicates that the battery is indeed charging.
Far Right - Current system time.