How do you connect two computers with Ethernet wire to play games by LAN?

If the computer both have LAN cards installed, you can simply use a crossover Cat5e/Cat6 network cable. Then set the IP addresses on each computer to be on the same subnet, e.g 192.168.1.1 and 192.168.1.2 with subnet mask 255.255.255.0.

Alternatively, you can set this up using a hub or switch and two straight through cables, wireless, along with other methods. This is not necessary if you only have two computers, but it may be more convenient.