1. Ping an external IP address. If you can ping an IP address, then you are connected to the Internet. Problem is probably DNS resolution. Check /etc/resolv.conf to make sure that you have an entry that starts with "nameserver" followed by the IP address of at least one of your DNS servers for your Internet connection.
2. If you can't ping an IP address, check to make sure you have a default gateway defined (run 'route' as root to find out). If no "default" route exists, add one.