As root, do
ifconfig
This will tell you if you have an IP, and how suse calls your eth card, which most likely will be eth0.
If you donīt have an IP, try
ifup eth0
and see if it grabs an IP.
If you already have one, try to ping google (64.233.187.104)
First with the name:
ping
www.google.com
If you can ping google by the name, you are set. If not, try with the IP:
ping 64.233.187.104
If you can ping google by the IP but not by the name, you need a DNS server set up.
Good luck, and keep us posted.