Linux Testing your network connection

1) First try pining your own IP address to see if your IP address is set properly, syntax is:
ping IP-ADDRESS

If your IP address is 202.54.1.10 then try:
# ping 202.54.1.10

Tip use ifconfig command to see IP address for eth0 or any other interface.

2) Try pinging neighboring machines IP addresses:
# ping 192.168.1.2 # ping 202.54.1.12
If you need to setup/configure network or connecting to the network under Linux use following tools:
Under Red Hat use neat OR system-config-network (Fedora core) command
Uder Debian Linux use network-admin command.

You can also start above command from GUI. Using above GUI tools you should able to configure DNS, hosts, IP address etc. For more information see:
List of LINUX troubleshooting commands/tools part # 1