welcome to LQ!
First, please describe how you connect to the internet. eg Do you have a cable modem, DSL, dial-up.? Does the connection use static IP or DHCP? Do you have a router?
Wireless or wired?
Provide as much detail as you can.
Fedora 6 is now pretty old, but there should be no issue getting a basic connection. Have you looked at the network section in the settings?