If your intention is to play games on PCs located in the same Local Area network and all devices are separated by just one single Router/layer 3 Device then all you have to do is to run a local DHCP server ( usually your Router ) , and set all systems to acquire IP address settings automatically. (like WhiteStar suggested )
The DHCP server will act as a central authority and will provide an IP configuration to anyone asking for it.
Also ensure that the ports your games require are not blocked on your router/machines. ( By default , it is not )
Now , if you want to play it over Routers , i.e. WAN , then you'll probably need certain softwares like "hamachi" or tungle.
In case if you want to configure manually and not through DHCP/router then just configure this in Network Adapter->Ipv4 settings in each of the hosts.
IP range : 192.168.172.1 - 192.168.172.254 or 172.16.0.1-172.31.255.254 or 10.0.0.1-10.255.255.254 ( assign host/machine a separate IP )
Gateway : Not required in case if you don't have a Router/gateway device for internet.
Subnet mask : 255.255.255.0 or 255.255.0.0 or 255.0.0.0 respectively.
This method worked for me in CS 1.6 (1PC and 1 Laptop, with BSNL provided modem)
Just plug in the laptop with a LAN cable to router, and plug in PC to the same router via lan cable, done...as simple as that, then open your game(cs in my case) and play, no need to do anything differently, and im pretty sure you knwo how to open play via lan In game settings n stuff
Usually it's as simple as that , but in certain cases where the machine is assigned a static IP , then you may need to configure either all the machines with Static Ip settings or else , enable DHCP service on router and set each host to acquire IP through DHCP service.