This is probably the most difficult part of the whole operation and if you can crack this, the rest should be relatively straightforward.
If you have a permanently connected router/firewall that runs DHCP for your intenet connection, this is much more straightforward as you can leave it as 'obtain an IP address automatically' and each PC will automatically grab an IP address from the DHCP server (your firewall/router).
You need to check that the TCP/IP protocol is installed on the system and bound to your network adapter. This is in the Network section in the control panel which should look something like this:

If TCP/IP isn't installed then you need to add the protocol by clicking the Add... button. Windows should automatically bind the TCP/IP protocol to the adapter.
Once installed (probably after a restart) then you need to select the TCP/IP -> Ethernet adapter and modify the properties.
Under the IP address tab, enable the specify an IP address then fill in the IP address as 192.168.0.x where x is a number from 1 to 255 and different for each PC. Fill in the subnet mask as 255.255.255.0 just like below:

Then under the Gateway tab add the gateway 192.168.0.0 which should be the same for all PCs. Next, under the Bindings tab, disable the File and sharing for Microsoft Networks. This is a security precaution to prevent outside access via TCP/IP by hackers etc. I'd still recommend using a reasonable firewall program such as @Guard (now Norton Internet Security), ZoneAlarm or a hardware firewall.

You'll need a restart after this.
The next step is to create a hosts file in your windows directory so you don't have to use IP addresses for local machines, only names. Some TCP/IP configurations allow name resolution over the network without a hosts file which is much less of a pain to administer as you don't have to keep editing the hosts file on every machine on your network. As an aside, you can use the hosts file as a local DNS lookup which makes web browsing quicker. Use a text editor such as notepad to create a file called hosts (no extension). It should look something like this:
#Small office network hosts file
#
localhost 127.0.0.1
#
192.168.0.1 secretary
192.168.0.2 production
192.168.0.3 accounts
192.168.0.4 sales
Lines starting with # are a comment and will be ignored. Match the IP adress for each machine specified above with the correct computer name you use on the network. Make sure you have the localhost 127.0.0.1 entry as it is a standard for the local PC. Save the file then copy it into each PC's windows directory (e.g., c:\windows).
Test the TCP/IP network by opening a DOS box and trying to ping a machine e.g., sales as follows:

If all is well then you should get a response as above.