I have installed TCP/IP, what steps should I use to verify the setup is correct?

From a command prompt type
ipconfig /all
This will show information such as IP address, subnet mask and the physical address. Check the IP address and subnet mask are what you expect.

Next there is a special IP address that is used for loopback testing 127.0.0.1, so try and ping this
ping 127.0.0.1
You should get 4 lines of
Reply from 127.0.0.1: bytes=32 time<10ms TTL=128
Pinging 127.0.0.1 does not send any traffic out on the network. If this does not work it means the TCP/IP stack is not loaded correctly so go back and check your configuration

Next try and ping your own IP address, once again this will not send any traffic out on the Network, but it just confirms the software
ping 200.200.200.53
Once again you should get 4 reply messages. If this does not work, but the loopback did, you probably have typed the IP address wrong, go back and check your configuration.

Try and ping the gateway.
ping 200.200.200.1
This is the first traffic going out over the network. The gateway should be on your subnet. If you fail to ping the gateway, check the gateway is up, and that your network is correctly connected.

Ping something on the other side of the gateway, i.e. something not own your subnet
ping 158.234.26.46
If this does not work then the gateway may not be functioning correctly.

If all of the above worked, than Name Resolution should be tested by pinging by name, this will test the HOSTS and/or DNS. If your machine name was john, and the domain savilltech.com, you would ping john.savilltech.com
ping john.savilltech.com
If this does not work, check in the Network Settings - Protocols - TCP/IP that the domain name is correct, also check the hosts file and the DNS.

Next try and ping a name outside the network
ping www.windows2000faq.com
If this does not work then check with your ISP (Internet Service Provider). Also make sure the site you are trying to ping supports ICMP or PING will not work.

If all of the above works then get down to the serious stuff and start surfing! :-)