Router vs wireless router

Here's a better description of the proper network topology for your setup:

1. Starting from your cable modem, there should be a Cat 5 cable that goes from the modem to the Uplink/Internet port on the back of your router. This port is usually separated from the rest of the ports on the router.

2. From the router, you should have one cable connected to the Uplink/Internet port, and another connected in any 1 of the other ports. This cable should be attached (at the other end) to your desktop computer.

By default, you should be able to connect to your router wirelessly from your notebook - look at your router manual for the SSID or network name. Use Windows to browse through available networks to find that name.
You do not want to keep the router in operation in this mode - other people can easily connect to your network, use your internet connection, access your computers, and all of your sent data! You should encrypt and lock the connection as soon as possible. Your router setup page should cover this - consult your manual.